Chapter XVII (1)

HISTORY OF PHYSICAL AND MISCELLANEOUS LITERATURE, FROM 1500 TO 1600.

SECT. I.--ON MATHEMATICAL AND PHYSICAL SCIENCE.

_Algebraists of this Period--Vieta--Slow Progress of Copernican Theory--Tycho Brahe--Reform of Calendar--Mechanics--Stevinus--Gilbert._

|Tartaglia and Cardan.|

1. The breach of faith towards Tartaglia, by which Cardan communicated to the world the method of solving cubic equations, having rendered them enemies, the injured party defied the aggressor to a contest, wherein each should propose thirty-one problems to be solved by the other. Cardan accepted the challenge, and gave a list of his problems, but devolved the task of meeting his antagonist on his disciple Ferrari. The problems of Tartaglia are so much more difficult than those of Cardan, and the latter’s representative so frequently failed in solving them, as to show the former in a higher rank among algebraists, though we have not so long a list of his discoveries.[1345] This is told by himself in a work of miscellaneous mathematical and physical learning, Quesiti ed invenzioni diverse, published in 1546. In 1555, he put forth the first part of a treatise intitled Trattato di numeri e misure, the second part appearing in 1560.

[1345] Montucla, p. 568.

|Algebra of Pelletier.|

2. Pelletier of Mans, a man advantageously known both in literature and science, published a short treatise on algebra in 1554. He does not give the method of solving cubic equations, but Hutton is mistaken in supposing that he was ignorant of Cardan’s work, which he quotes. In fact he promises a third book, this treatise being divided into two, on the higher parts of algebra; but I do not know whether this be found in any subsequent edition. Pelletier does not employ the signs + and -, which had been invented by Stifelies, using _p_ and _m_ instead, but we find the sign √ of irrationality. What is perhaps the most original in this treatise, is that its author perceived that, in a quadratic equation, where the root is rational, it must be a divisor of the absolute number.[1346]

[1346] Pelletier seems to have arrived at this not by observation, but
in a scientific method. Comme _x_² = 2_x_ + 15. (I substitute the
usual signs for clearness), il est certain que _x_ que nous
cherchons doit estre contenu également en 15, puisque _x_² est égal
à deux _x_, et 15 davantage, et que tout nombre _censique_ (quarré)
contient les racines également et précisément. Maintenant puisque 2
_x_ font certain nombre de racines, il faut donc que 15 fasse
l’achèvement des racines qui sont nécessaires pour accomplir _x_².
p. 40. (Lyon, 1554.)

|Record’s Whetstone of Wit.|

3. In the Whetstone of Wit, by Robert Record, in 1557, we find the signs + and -, and, for the first time, that of equality =, which he invented.[1347] Record knew that a quadratic equation has two roots. The scholar, for it is in dialogue, having been perplexed by this as a difficulty, the master answers, “That variety of roots doth declare that one equation in number may serve for two several questions. But the form of the question may easily instruct you which of these two roots you shall take for your purpose. Howbeit, sometimes you may take both.”[1348] He says nothing of cubic equations, having been prevented by an interruption, the nature of which he does not divulge, from continuing his algebraic lessons. We owe therefore nothing to Record but his invention of a sign. As these artifices not only abbreviate, but clear up the process of reasoning, each successive improvement in notation deserves, even in the most concise sketch of mathematical history, to be remarked. But certainly they do not exhibit any peculiar ingenuity, and might have occurred to the most ordinary student.

[1347] “And to avoid the tedious repetition of these words, “is equal
to,” I will set, as I do often in work use, a pair of parallels,
_gemowe_ lines of one length thus =, because no two things can be
more equal.” The word _gemowe_, from the French _gemeau_, twin
(Cotgrave) is very uncommon: it was used for a double ring, a
_gemel_ or _gemou_ ring. Todd’s Johnson’s Dictionary.

[1348] This general mode of expression might lead us to suppose, that
Record was acquainted with negative, as well as positive roots, the
fictæ radices of Cardan. That a quadratic equation of a certain
form has two positive roots, had long been known. In a very modern
book, it is said that Mohammed ben Musa, an Arabian of the reign of
Almamon, whose algebra was translated by the late Dr. Rosen in
1831, observes that there are two roots in the form _ax_² + _b_ =
_cx_, but that this cannot be in the other three cases. Libri,
Hist. des Sciences Mathématiques en Italie, vol. ii. (1838).
Leonard of Pisa had some notion of this, but did not state it,
according to M. Libri, so generally as Ben Musa. Upon reference to
Colebrook’s Indian Algebra, it will appear that the existence of
two positive roots in some cases, though the conditions of the
problem will often be found to exclude the application of one of
them, is clearly laid down by the Hindoo algebraists. But one of
them says, “People do not approve a negative absolute number.”

|Vieta.|

|His discoveries.|

4. The great boast of France, and indeed of algebraical science generally, in this period, was Francis Viète, oftener called Vieta, so truly eminent a man that he may well spare laurels which are not his own. It has been observed in another place, that after Montucla had rescued from the hands of Wallis, who claims everything for Harriott, many algebraical methods indisputably contained in the writings of his own countryman, Cossali has stepped forward, with an equal cogency of proof, asserting the right of Cardan to the greater number of them. But the following steps in the progress of algebra may be justly attributed to Vieta alone. 1. We must give the first place to one less difficult in itself, than important in its results. In the earlier algebra, alphabetical characters were not generally employed at all, except that the Res, or unknown quantity, was sometimes set down R. for the sake of brevity. Stifelius, in 1544, first employed a literal notation, A. B. C. to express unknown quantities, while Cardan, and according to Cossali, Luca di Borgo, to whom we may now add Leonard of Pisa himself, make some use of letters to express indefinite numbers.[1349] But Vieta first applied them as general symbols of quantity, and by thus forming the scattered elements of specious analysis into a system, has been justly reckoned the founder of a science, which, from its extensive application, has made the old problems of mere numerical algebra appear elementary and almost trifling. “Algebra,” says Kästner, “from furnishing amusing enigmas to the Cossists,” as he calls the first teachers of the art, “became the logic of geometrical invention.”[1350] It would appear a natural conjecture, that the improvement, towards which so many steps had been taken by others, might occur to the mind of Vieta simply as a means of saving the trouble of arithmetical operations in working out a problem. But those who refer to his treatise entitled, De Arte Analytica isagoge, or even the first page of it, will, I conceive, give credit to the author for a more scientific view of his own invention. He calls it logistice speciosa, as opposed to the logistice numerosa of the older analysis;[1351] his theorems are all general, the given quantities being considered as indefinite, nor does it appear that he substituted letters for the known quantities in the investigation of particular problems. Whatever may have suggested this great invention to the mind of Vieta, it has altogether changed the character of his science.

[1349] Vol. i. p. 54. A modern writer has remarked, that Aristotle
employs letters of the alphabet to express indeterminate
quantities, and says it has never been observed before. He refers
to the Physics, in Aristot. Opera, i. 543, 550, 565, &c., but
without mentioning any edition. The letters α [alpha], β [beta], γ
[gamma], &c. express force, mass, space or time. Libri, Hist. des
Sciences Mathématiques en Italie, i. 104. Upon reference to
Aristotle, I find many instances in the sixth book of the Physicæ
Auscultationes, and in other places.

Though I am reluctant to mix in my text which is taken from
established writers, any observations of my own on a subject
wherein my knowledge is so very limited as in mathematics, I may
here remark, that although Tartaglia and Cardan do not use single
letters as symbols of known quantity, yet, when they refer to a
geometrical construction, they employ in their equations double
letters, the usual signs of lines. Thus we find, in the Ars Magna,
AB _m_ AC, where we should put _a_ - _b_. The want of a good algorithm
was doubtless a great impediment, but it was not quite so deficient
as from reading modern histories of algebraical discovery, without
reference to the original writers, we might be led to suppose.

The process by which the rule for solving cubic equations was
originally discovered, seems worthy, as I have intimated in another
place (p. 221), of exciting our curiosity. Maseres has investigated
this in the Philosophical Transactions for 1780, reprinted in his
Tracts on Cubic and Biquadratic Equations, p. 55-69, and in
Scriptores Logarithmici, vol. ii. It is remarkable, that he does
not seem to have been aware of what Cardan has himself told us on
the subject in the sixth chapter of the Ars Magna; yet he has
nearly guessed the process which Tartaglia pursued; that is, by a
geometrical construction. It is manifest, by all that these
algebraists have written on the subject, that they had the clearest
conviction they were dealing with continuous, or geometrical, not
merely with discreet, or arithmetical, quantity. This gave them an
insight into the fundamental truth, which is unintelligible so long
as algebra passes for a specious _arithmetic_, that _every_ value,
which the conditions of the problem admit, may be assigned to
unknown quantities, without distinction of rationality and
irrationality. To abstract number itself irrationality is
inapplicable.

[1350] Geschichte der Mathematik, i. 63.

[1351] Forma autem Zetesin ineundi ex arte propria est, non jam in
numeris suam logicam exercente, quæ fuit oscitantia veterum
analystarum, sed per logisticen sub specie noviter inducendam,
feliciorem multo et potiorem numerosa, ad comparandum inter se
magnitudines, proposita primum homogeniorum lege, &c. p. i. edit.
1646.

A profound writer on algebra, Mr. Peacock, has lately defined it,
“the science of general reasoning by symbolical language.” In this
sense there was very little algebra before Vieta, and it would be
improper to talk of its being known to the Greeks, Arabs, or
Hindoos. The definition would also include the formulas of logic.
The original definition of algebra seems to be, the science of
finding an equation between known and unknown quantities, per
oppositionem et restaurationem.

5. Secondly, Vieta understood the transformation of equations, so as to clear them from coefficients or surd roots, or to eliminate the second term. This however is partly claimed by Cossali for Cardan. Yet it seems that the process employed by Cardan was much less neat and short than that of Vieta, which is still in use.[1352] 3. He obtained a solution of cubic equations in a different method from that of Tartaglia. 4. “He shows,” says Montucla, “that when the unknown quantity of any equation may have several positive values, for it must be admitted that it is only these that he considers, the second term has for its coefficient the sum of these values with the sign -, the third has the sum of the products of these values multiplied in pairs; the fourth the sum of such products multiplied in threes, and so forth; finally, that the absolute term is the product of all the values. Here is the discovery of Harriott pretty nearly made.” It is at least no small advance towards it.[1353] Cardan is said to have gone some way towards this theory, but not with much clearness, nor extending it to equations above the third degree. 5. He devised a method of solving equations by approximation, analogous to the process of extracting roots, which has been superseded by the invention of more compendious rules.[1354] 6. He has been regarded by some as the true author of the application of algebra to geometry, giving copious examples of the solution of problems by this method, though all belonging to straight lines. It looks like a sign of the geometrical relation under which he contemplated his own science, that he uniformly denominates the first power of the unknown quantity _latus_. But this will be found in older writers.[1355]

[1352] It is fully explained in his work De Recognitione Æquationum,
cap. 7.

[1353] Some theorems given by Vieta very shortly and without
demonstration, show his knowledge of the structure of equations. I
transcribe from Maseres, who has expressed them in the usual
algebraic language. Si _a_ + _b_ × _x_ - _x_² æquetur _ab_, _x_
explicabilis est de qualibet illarum duarum _a_ vel _b_. The second
theorem is:--

a} ab}
Si x³ - b}x² + ac}x
c} bc}

æquetur _abc_, _x_ explicabilis est de qualibet illarum trium _a_,
_b_, vel _c_. The third and fourth theorems extend this to higher
equations.

[1354] Montucla, i. 600. Hutton’s Mathematical Dictionary. Biog.
Univers. art. Viète.

[1355] It is certain that Vieta perfectly knew the relation of algebra
to magnitude as well as number, as the first pages of his In Artem
Analyticam Isagoge fully show. But it is equally certain that
Tartaglia and Cardan, and much older writers, Oriental as well as
European, knew the same; it was by help of geometry, which Cardan
calls _via regia_, that the former made his great discovery of the
solution of cubic equations. Cossali, ii. 147. Cardan, Ars Magna,
ch. xi.

_Latus_ and _radix_ are used indifferently for the first power of
the unknown quantity in the Ars Magna. Cossali contends that Fra
Luca had applied algebra to geometry. Vieta, however, it is said,
was the first who taught how to construct geometrical figures by
means of algebra, Montucla, p. 604. But compare Cossali, p. 427.

A writer lately quoted, and to whose knowledge and talents I bow
with deference, seems, as I would venture to suggest, to have
overrated the importance of that employment of letters to signify
quantities, known or unknown, which he has found in Aristotle, and
in several of the moderns, and in consequence to have depreciated
the real merit of Vieta. Leonard of Pisa, it seems, whose algebra
this writer has for the first time published, to his own honour and
the advantage of scientific history, makes use of letters as well
as lines, to represent quantities. Quelquefois il emploie des
lettres pour exprimer des quantités indéterminées, connues ou
inconnues, sans les représenter par des lignes. On voit ici comment
les modernes ont été amenés à se servir des lettres d’Alphabet
(même pour exprimer des quantités connues) long temps avant Viète,
à qui on a attribué à tort une notation qu’il faudrait peut-être
faire remonter jusqu’à Aristote, et que tant d’Algébraistes
modernes ont employée avant le géomètre Français. Car outre Leonard
di Pise, Paciolo et d’Autres géomètres Italiens firent usage des
lettres pour indiquer les quantités connues, et c’est d’eux plutôt
que d’Aristote que les modernes ont appris cette notation. Libri,
vol. ii. p. 34. But there is surely a wide interval between the use
of a short symbolic expression for particular quantities, as M.
Libri has remarked in Aristotle, or even the _partial_ employment
of letters to designate known quantities, as in the Italian
algebraists, and the method of stating general relations by the
exclusive use of letters, which Vieta first introduced. That
Tartaglia and Cardan, and even, as it now appears, Leonard of Pisa
went a certain way towards the invention of Vieta, cannot much
diminish his glory; especially when we find that he entirely
apprehended the importance of his own logistice speciosa in
science. I have mentioned above, that, as far as my observation has
gone, Vieta does not work particular problems by the specious
algebra.

6. “Algebra,” says a philosopher of the present day, “was still only an ingenious art, limited to the investigation of numbers; Vieta displayed all its extent, and instituted general expressions for particular results. Having profoundly meditated on the nature of algebra, he perceived that the chief characteristic of the science is to express relations. Newton with the same idea defined algebra an universal arithmetic. The first consequences of this general principle of Vieta were his own application of his specious analysis to geometry, and the theory of curve lines, which is due to Descartes; a fruitful idea, from which the analysis of functions, and the most sublime discoveries, have been deduced. It has led to the notion that Descartes is the first who applied algebra to geometry; but this invention is really due to Vieta; for he resolved geometrical problems by algebraic analysis, and constructed figures by means of these solutions. These investigations led him to the theory of angular sections, and to the general equations which express the values of chords.”[1356] It will be seen in the notes that some of this language requires a slight limitation.

[1356] M. Fourier, quoted in Biographie Universelle.

7. The Algebra of Bombelli, published in 1589, is the only other treatise of the kind during this period that seems worthy of much notice. Bombelli saw better than Cardan the nature of what is called the irreducible case in cubic equations. But Vieta, whether after Bombelli or not, is not certain, had the same merit.[1357] It is remarkable that Vieta seems to have paid little regard to the discoveries of his predecessors. Ignorant, probably, of the writings of Record, and perhaps even of those of Stifelius, he neither uses the sign = of equality, employing instead the clumsy word Æquatio, or rather Æquetur,[1358] nor numeral exponents; and Hutton observes that Vieta’s algebra has, in consequence, the appearance of being older than it is. He mentions, however, the signs + and -, as usual in his own time.

[1357] Cossali. Hutton.

[1358] Vieta uses =, but it is to denote that the proposition is true
both of + and -; where we put ±. It is almost a presumption of
copying one from another, that several modern writers say Vieta’s
word is _æquatio_. I have always found it _æquetur_; a difference
not material in itself.

|Geometers of this period.|

8. Amidst the great progress of algebra through the sixteenth century, the geometers, content with what the ancients had left them, seem to have had little care but to elucidate their remains. Euclid was the object of their idolatry; no fault could be acknowledged in his elements, and to write a verbose commentary upon a few propositions was enough to make the reputation of a geometer. Among the almost innumerable editions of Euclid that appeared, those of Commandin and Clavius, both of them in the first rank of mathematicians for that age, may be distinguished. Commandin, especially, was much in request in England, where he was frequently reprinted, and Montucla calls him the model of commentators for the pertinence and sufficiency of his notes. The commentary of Clavius, though a little prolix, acquired a still higher reputation. We owe to Commandin editions of the more difficult geometers, Archimedes, Pappus, and Apollonius; but he attempted little, and that without success, beyond the province of a translator and a commentator. Maurolycus of Messina had no superior among contemporary geometers. Besides his edition of Archimedes, and other labours on the ancient mathematicians, he struck out the elegant theory, in which others have followed him, of deducing the properties of the conic sections from those of the cone itself. But we must refer the reader to Montucla, and other historical and biographical works, for the less distinguished writers of the sixteenth age.[1359]

[1359] Montucla. Kästner. Hutton. Biogr. Univ.

|Joachim Rhæticus.|

9. The extraordinary labour of Joachim Rhæticus in his trigonometrical calculations, has been mentioned in our first volume. His Opus Palatinum de Triangulis was published from his manuscript by Valentine Otho, in 1594. But the work was left incomplete, and the editor did not accomplish what Joachim had designed. In his tables the sines, tangents, and secants are only calculated to ten, instead of fifteen places of decimals. Pitiscus, in 1613, not only completed Joachim’s intention, but carried the minuteness of calculation a good deal farther.[1360]

[1360] Montucla, p. 581.

|Copernican theory.|

10. It can excite no wonder that the system of Copernicus, simple and beautiful as it is, met with little encouragement for a long time after its promulgation, when we reflect upon the natural obstacles to its reception. Mankind can in general take these theories of the celestial movements only upon trust from philosophers; and in this instance it required a very general concurrence of competent judges to overcome the repugnance of what called itself common sense, and was in fact a prejudice as natural, as universal, and as irresistible as could influence human belief. With this was united another, derived from the language of Scripture; and though it might have been sufficient to answer, that phrases implying the rest of the earth and motion of the sun are merely popular, and such as those who are best convinced of the opposite doctrine must employ in ordinary language, this was neither satisfactory to the vulgar, nor recognised by the church. Nor were the astronomers in general much more favourable to the new theory than either the clergy or the multitude. They had taken pains to familiarise their understandings with the Ptolemaic hypothesis; and it may be often observed that those who have once mastered a complex theory are better pleased with it than with one of more simplicity. The whole weight of Aristotle’s name, which, in the sixteenth century, not only biassed the judgment, but engaged the passions, connected as it was with general orthodoxy and preservation of established systems, was thrown into the scale against Copernicus. It was asked what demonstration could be given of his hypothesis; whether the movements of the heavenly bodies could not be reconciled to the Ptolemaic; whether the greater quantity of motion, and the complicated arrangement which the latter required, could be deemed sufficient objections to a scheme proceeding from the Author of nature, to whose power and wisdom our notions of simplicity and facility are inapplicable; whether the moral dignity of man, and his peculiar relations to the Deity, unfolded in Scripture, did not give the world he inhabits a better claim to the place of honour in the universe, than could be pretended, on the score of mere magnitude, for the sun. It must be confessed, that the strongest presumptions in favour of the system of Copernicus were not discovered by himself.

11. It is easy, says Montucla, to reckon the number of adherents to the Copernican theory during the sixteenth century. After Rhæticus, they may be nearly reduced to Reinold, author of the Prussian tables; Rothman, whom Tycho drew over afterwards to his own system; Christian Wursticius (Ursticius), who made some proselytes in Italy; finally, Mæstlin, the illustrious master of Kepler. He might have added Wright and Gilbert, for the credit of England. Among the Italian proselytes made by Wursticius, we may perhaps name Jordano Bruno, who strenuously asserts the Copernican hypothesis; and two much greater authorities in physical science, Benedetti and Galileo himself. It is evident that the preponderance of valuable suffrages was already on the side of truth.[1361]

[1361] Montucla, p. 638.

|Tycho Brahe.|

12. The predominant disinclination to contravene the apparent testimonies of sense and Scripture had, perhaps, more effect than the desire of originality in suggesting the middle course taken by Tycho Brahe. He was a Dane of noble birth, and early drawn by the impulse of natural genius to the study of astronomy. Frederic III., his sovereign, after Tycho had already obtained some reputation, erected for him the observatory of Uraniburg in a small isle of the Baltic. In this solitude he passed above twenty years, accumulating the most extensive and accurate observations which were known in Europe before the discovery of the telescope and the improvement of astronomical instruments. These, however, were not published till 1606, though Kepler had previously used them in his Tabulæ Rodolphinæ. Tycho himself did far more in this essential department of the astronomer than any of his predecessors; his resources were much beyond those of Copernicus, and the latter years of this century may be said to make an epoch in physical astronomy. Frederic, Landgrave of Hesse, was more than a patron of the science. The observations of that prince have been deemed worthy of praise long after his rank had ceased to avail them. The emperor Rodolph, when Tycho had been driven by envy from Denmark, gave him an asylum and the means of carrying on his observations at Prague, where he died in 1601. He was the first in modern times who made a catalogue of stars, registering their positions as well as his instruments permitted him. This catalogue, published in his Progymnasmata in 1602, contained 777, to which, from Tycho’s own manuscripts, Kepler added 223 stars.[1362]

[1362] Montucla, p. 653-659.

|His system.|

13. In the new mundane system of Tycho Brahe, which, though first regularly promulgated to the world in his Progymnasmata, had been communicated in his epistles to the Landgrave of Hesse, he supposes the five planets to move round the sun, but carries the sun itself with these five satellites, as well as the moon, round the earth. Though this, at least at the time, might explain the known phenomena as well as the two other theories, its want of simplicity always prevented its reception. Except Longomontanus, the countryman and disciple of Tycho, scarce any conspicuous astronomer adopted an hypothesis which, if it had been devised some time sooner, would perhaps have met with better success. But in the seventeenth century, the wise all fell into the Copernican theory, and the many were content without any theory at all.

14. A great discovery in physical astronomy may be assigned to Tycho. Aristotle had pronounced comets to be meteors generated below the orbit of the moon. But a remarkable comet in 1577 having led Tycho to observe its path accurately, he came to the conclusion that these bodies are far beyond the lunar orbit, and that they pass through what had always been taken for a solid firmament, environing the starry orbs, and which plays no small part in the system of Ptolemy. He was even near the discovery of their elliptic revolution; the idea of a curve round the sun having struck him, though he could not follow it by observation.[1363]

[1363] Montucla, p. 662.

|Gregorian calendar.|

15. The acknowledged necessity of reforming the Julian calendar gave in this age a great importance to astronomy. It is unnecessary to go into the details of this change, effected by the authority of Gregory XIII., and the skill of Lilius and Clavius, the mathematicians employed under him. The new calendar was immediately received in all countries acknowledging the pope’s supremacy; not so much on that account, though a discrepancy in the ecclesiastical reckoning would have been very inconvenient, as of its real superiority over the Julian. The protestant countries came much more slowly into the alteration; truth being no longer truth, when promulgated by the pope. It is now admitted that the Gregorian calendar is very nearly perfect, at least as to the computation of the solar year, though it is not quite accurate for the purpose of finding Easter. In that age, it had to encounter the opposition of Mæstlin, an astronomer of deserved reputation, and of Scaliger, whose knowledge of chronology ought to have made him conversant with the subject, but who, by a method of squaring the circle, which he announces with great confidence as a demonstration, showed the world that his genius did not guide him to the exact sciences.[1364]

[1364] Montucla, p. 674-686.

|Optics.|

16. The science of optics, as well as all other branches of the mixed mathematics, fell very short of astronomy in the number and success of its promoters. It was carried not much farther than the point where Alhazen, Vitello, and Roger Bacon left it. Maurolycus of Messina, in a treatise published in 1575, though written, according to Montucla, fifty years before, entitled Theoremata de Lumine et Umbra, has mingled a few novel truths with error. He explains rightly the fact that a ray of light, received through a small aperature of any shape, produces a circular illumination on a body intercepting it at some distance; and points out why different defects of vision are remedied by convex or concave lenses. He had however mistaken notions as to the visual power of the eye, which he ascribed not to the retina but to the crystalline humour; and on the whole, Maurolycus, though a very distinguished philosopher in that age, seems to have made few considerable discoveries in physical science.[1365] Baptista Porta, who invented, or at least made known, the camera obscura, though he dwells on many optical phenomena in his Magia Naturalis, sometimes making just observations, had little insight into the principles that explain them.[1366] The science of perspective has been more frequently treated, especially in this period, by painters and architects than by mathematicians. Albert Durer, Serlio, Vignola, and especially Peruzzi, distinguished themselves by practical treatises; but the geometrical principles were never well laid down before the work of Guido Ubaldi in 1600.[1367]

[1365] Id. p. 695.

[1366] Montucla, p. 698.

[1367] Id. p. 708.

|Mechanics.|

17. This author, of a noble family in the Apennines, ranks high also among the improvers of theoretical mechanics. This great science, checked, like so many others, by the erroneous principles of Aristotle, made scarce any progress till near the end of the century. Cardan and Tartaglia wrote upon the subject; but their acuteness in abstract mathematics did not compensate for a want of accurate observation and a strange looseness of reasoning. Thus Cardan infers that the power required to sustain a weight on an inclined plane varies in the exact ratio of the angle, because it vanishes when the plane is horizontal, and becomes equal to the weight when the plane is perpendicular. But this must be the case if the power follows any other law of direct variation, as that of the sine of inclination, that is, the height, which it really does.[1368] Tartaglia, on his part, conceived that a cannon-ball did not indeed describe two sides of a parallelogram, as was commonly imagined even by scientific writers, but, what is hardly less absurd, that its point-blank direction and line of perpendicular descent are united by a circular arch, to which they are tangents. It was generally agreed, till the time of Guido Ubaldi, that the arms of a lever charged with equal weights, if displaced from the horizontal position, would recover it when set at liberty. Benedetti of Turin had juster notions than his Italian contemporaries; he ascribed the centrifugal force of bodies to their tendency to move in a straight line; he determined the law of equilibrium for the oblique lever, and even understood the composition of motions.[1369]

[1368] Id. p. 690.

[1369] Montucla, p. 693.

18. If, indeed, we should give credit to the sixteenth century for all that was actually discovered, and even reduced to writing, we might now proceed to the great name of Galileo. For it has been said that his treatise Della Scienza Mechanica was written in 1592, though not published for more than forty years afterwards.[1370] But as it has been our rule, with not many exceptions, to date books from their publication, we must defer any mention of this remarkable work to the next volume. The experiments, however, made by Galileo, when lecturer in mathematics at Pisa, on falling bodies, come strictly within our limits. He was appointed to this office in 1589, and left it in 1592. Among the many unfounded assertions of Aristotle in physics, it was one that the velocity of falling bodies was proportionate to their weights; Galileo took advantage of the leaning tower of Pisa to prove the contrary. But this important, though obvious experiment, which laid open much of the theory of motion, displeased the adherents of Aristotle so highly, that they compelled him to leave Pisa. He soon obtained a chair in the university of Padua.

[1370] Playfair has fallen into the mistake of supposing that this
treatise was _published_ in 1592; and those who, on second
thoughts, would have known better, have copied him.

|Statics of Stevinus.|

19. But on the same principle that we exclude the work of Galileo on mechanics from the sixteenth century, it seems reasonable to mention that of Simon Stevinus of Bruges; since the first edition of his Statics and Hydrostatics was printed in Dutch as early as 1585, though we can hardly date its reception among the scientific public before the Latin edition in 1608. Stevinus has been chiefly known by his discovery of the law of equilibrium on the inclined plane, which had baffled the ancients, and, as we have seen, was mistaken by Cardan. Stevinus supposed a flexible chain of uniform weight to descend down the sides of two connected planes, and to hang in a sort of festoon below. The chain would be in equilibrio, because, if it began to move, there would be no reason why it should not move for ever, the circumstances being unaltered by any motion it could have; and thus there would be a perpetual motion, which is impossible. But the part below, being equally balanced, must, separately taken, be in equilibrio. Consequently the part above, lying along the planes, must also be in equilibrio; and hence the weight of the two parts of the chain must be equal, or if that lying along the shorter plane be called the power, it will be to the other as the lengths; or if there be but one plane, and the power hang perpendicularly, as the height to the length.

20. It has been doubted whether this demonstration of Stevinus be satisfactory, and also whether the theorem had not been proved in a different manner by an earlier writer. The claims of Stevinus, however, have very recently been maintained by an author of high reputation.[1371] The Statics of this ingenious mathematician contain several novel and curious theorems on the properties of other mechanical powers besides the inclined plane. But Montucla has attributed to him what I cannot find in his works. “In resolving these questions (concerning the ratios of weights on the oblique pulley), and several others, he frequently makes use of the famous principle which is the basis of the Nouvelle Mécanique of M. Varignon. He forms a triangle, of which the three sides are parallel to the three directions, namely, of the weight and the two powers which support it; and he shows that these three lines express this weight and these powers respectively.”[1372] Playfair, copying Montucla, I presume, without looking at Stevinus, has repeated this statement, and it will be found in other modern histories of physical science. This theorem, however, of Varignon, commonly called the triangle of forces, will not, unless I am greatly mistaken, be discovered in Stevinus. Had it been known to him, we may presume that he would have employed it, as is done in modern works on mechanics, for demonstrating the law of equilibrium on the inclined plane, instead of his catenarian hypothesis, which is at least not so elegant or capable of so simple a proof. It is true that in treating of the oblique pulley, he resolves the force into two, one parallel, the other perpendicular to the weight; and thus displays his acquaintance with the composition of forces. But whether he had a clear perception of all the dynamical laws, involved in the demonstration of Varignon’s theorem, may possibly be doubtful; at least, we do not find that he has employed it.

[1371] Playfair’s Dissertation. Whewell’s Hist. of Inductive Sciences,
ii. 11, 14. Compare Drinkwater’s Life of Galileo, p. 83. The
reasoning which Mr. W. suggests for Stevinus, whether it had
occurred to him or not, may be very just, but borders, perhaps,
rather too much on the metaphysics of science.

[1372] Montucla, ii. 180.

|Hydrostatics.|

21. The first discovery made in hydrostatics since the time of Archimedes is due to Stevinus. He found that the vertical pressure of fluids on a horizontal surface is as the product of the base of the vessel by its height, and showed the law of pressure even on the sides.[1373]

[1373] Montucla, ii. 180.

|Gilbert on the Magnet.|

22. The year 1600 was the first in which England produced a remarkable work in physical science; but this was one sufficient to raise a lasting reputation to its author. Gilbert, a physician, in his Latin treatise on the Magnet, not only collected all the knowledge which others had possessed on that subject, but became at once the father of experimental philosophy in this island, and by a singular felicity and acuteness of genius, the founder of theories which have been revived after the lapse of ages, and are almost universally received into the creel of the science. The magnetism of the earth itself, his own original hypothesis, nova illa nostra et inaudita de tellure sententia, could not, of course, be confirmed by all the experimental and analogical proof, which has rendered that doctrine accepted in recent philosophy; but it was by no means one of those vague conjectures that are sometimes unduly applauded, when they receive a confirmation by the favour of fortune. He relied on the analogy of terrestrial phenomena to those exhibited by what he calls a _terrella_, or artificial spherical magnet. What may be the validity of his reasonings from experiment it is for those who are conversant with the subject to determine, but it is evidently by the torch of experiment that he was guided. A letter from Edward Wright, whose authority as a mathematician is of some value, admits the terrestrial magnetism to be proved. Gilbert was also one of our earliest Copernicans, at least as to the rotation of the earth;[1374] and with his usual sagacity inferred, before the invention of the telescope; that there must be a multitude of fixed stars beyond the reach of our vision.[1375]

[1374] Mr. Whewell thinks that Gilbert was more doubtful about the
annual than the diurnal motion of the earth, and informs us that in
a posthumous work he seems to hesitate between Tycho and
Copernicus. Hist. of Inductive Sciences, i. 389. Gilbert’s argument
for the diurnal motion would extend to the annual. Non probabilis
modo sed manifesta videtur terræ diurna circumvolutio, cum natura
semper agit per pauciora magis quam plura, atque rationi magis
consentaneum videtur unum exiguum corpus telluris diurnam
volutationem efficere quam mundum totum circumferri.

[1375] l. 6. c. 3. The article on Gilbert in the Biographie Universelle
is discreditable to that publication. If the author was so very
ignorant as not to have known anything of Gilbert, he might at
least have avoided the assumption that nothing was to be known.

Sarpi, who will not be thought an incompetent judge, names Gilbert
with Vieta, as the only original writers among his contemporaries.
Non ho veduto in questo secolo uomo quale abbia scritto cosa sua
propria, salvo Vieta in Francia e Gilberti in Inghilterra. Lettere
di Fra Paolo, p. 31.

SECT. II.--ON NATURAL HISTORY.

_Zoology--Gesner, Aldrovandus. Botany--Lobel, Cæsalpin, and others._

|Gesner’s Zoology.|

23. Zoology and botany, in the middle of the sixteenth century, were as yet almost neglected fields of knowledge; scarce anything had been added to the valuable history of animals by Aristotle, and those of plants by Theophrastus and Dioscorides. But in the year 1551 was published the first part of an immense work, the History of Animals, by that prodigy of general erudition, Conrad Gesner. This treats of viviparous quadrupeds; the second, which appeared in 1554, of the oviparous; the third, in 1555, of birds; the fourth, in the following year, of fishes and aquatic animals; and one, long afterwards published in 1587, relates to serpents. The first part was reprinted with additions in 1560, and a smaller work of woodcuts and shorter descriptions, called Icones Animalium, appeared in 1553.

|Its character by Cuvier.|

24. This work of the first great naturalist of modern times is thus eulogised by one of the latest:--“Gesner’s History of Animals,” says Cuvier, “may be considered as the basis of all modern zoology; copied almost literally by Aldrovandus, abridged by Jonston, it has become the foundation of much more recent works; and more than one famous author has borrowed from it silently most of his learning; for those passages of the ancients, which have escaped Gesner, have scarce ever been observed by the moderns. He deserved their confidence by his accuracy, his perspicuity, his good faith, and sometimes by the sagacity of his views. Though he has not laid down any natural classification by genera, he often points out very well the true relations of beings.”[1376]

[1376] Biogr. Universelle, art. Gesner.

|Gesner’s arrangement.|

25. Gesner treats of every animal under eight heads or chapters: 1. Its name in different languages; 2. Its external description and usual place of habitation (or what naturalists call _habitat_); 3. Its natural actions, length of life, diseases, &c.; 4. Its disposition, or, as we may say, moral character; 5. Its utility, except for food and medicine; 6. Its use as food; 7. Its use in medicine; 8. The philological relations of the name and qualities, their proper and figurative use in language, which is subdivided into several sections. So comprehensive a notion of zoology displays a mind accustomed to encyclopedic systems, and loving the labours of learning for their own sake. Much of course would have a very secondary value in the eyes of a good naturalist. His method is alphabetical, but it may be reckoned an alphabet of genera; for he arranges what he deems cognate species together. In the Icones Animalium we find somewhat more of classification. Gesner divides quadrupeds into Animalia Mansueta and Animalia Fera; the former in two, the latter in four orders. Cuvier, in the passage above cited, writing probably from memory, has hardly done justice to Gesner in this respect. The delineations in the History of Animals and in the Icones are very rude; and it is not always easy, with so little assistance from engraving, to determine the species from his description.

|His additions to known quadrupeds.|

26. Linnæus, though professing to give the synonyms of his predecessors, has been frequently careless and unjust towards Gesner; his mention of several quadrupeds (the only part of the latter’s work at which I have looked), having been unnoticed in the Systema Naturæ. We do not find however that Gesner had made very considerable additions to the number of species known to the ancients; and it cannot be reckoned a proof of his acuteness in zoology, that he placed the hippopotamus among aquatic animals, and the bat among birds. In the latter extraordinary error he was followed by all other naturalists till the time of Ray. Yet he shows some judgment in rejecting plainly fabulous animals. In the edition of 1551 I find but few quadrupeds, except those belonging to the countries round the Mediterranean, or mentioned by Pliny and Ælian.[1377] The Reindeer, which it is doubtful whether the ancients knew, though there seems reason to believe that it was formerly an inhabitant of Poland and Germany, he found in Albertus Magnus; and from him too Gesner had got some notion of the Polar Bear. He mentions the Musk deer, which was known through the Arabian writers, though unnoticed by the ancients. The new world furnished him with a scanty list. Among these is the Opossum, or Semi-Vulpa (for which Linnæus has not given him credit), an account of which he may have found in Pinzon or Peter Martyr;[1378] the Manati, of which he found a description in Hernando’s History of the Indies; and the Guinea Pig, Cuniculus Indus, which he says was, within a few years, first brought to Europe from the New World, but was become everywhere common. In the edition of 1560, several more species are introduced. Olaus Magnus had, in the meantime, described the Glutton; and Belon had found an Armadillo among itinerant quacks in Turkey, though he knew that it came from America.[1379] Belon had also described the Axis deer of India. The Sloth appears for the first time in this edition of Gesner, and the Sagoin, or Ouistiti, as well as what he calls Mus Indicus alius, which Linnæus refers to the Racoon, but seems rather to be the Nasua, or Coati Mondi. Gesner has given only three cuts of monkeys, but was aware that there were several kinds, and distinguishes them in description. I have not presumed to refer his cuts to particular species, which probably, on account of their rudeness, a good naturalist would not attempt. The Simia Inues, or Barbary ape, seems to be one, as we might expect.[1380] Gesner was not very diligent in examining the histories of the New World. Peter Martyr and Hernando would have supplied him with several he has overlooked, as the Tapir, the Pecary, the Anteater, and the fetid Polecat.[1381]

[1377] In Cardan, De Subtilitate, lib. 10, published in 1550, I find
the anteater, ursus formicarius, which, if I am not mistaken,
Gesner has omitted, though it is in Hernando d’Oviedo; also a
cercopithecus, as large as man, which persists long in standing
erect, amat pueros et mulieres, conaturque concumbere, quod nos
vidimus. This was probably one of the large baboons of Africa.

[1378] In the voyage of Pinzon, the companion of Columbus in his last
voyage, when the continent of Guiana was discovered, which will be
found in the Novus Orbis of Grynæus, a specimen of the genus
Didelphis is mentioned with the astonishment which the first
appearance of the marsupial type would naturally excite in a
European. Conspexere etiamnum ibi animal quadrupes, prodigiosum
quidem; nam pars anterior vulpem, posterior vero simiam
præsentabat, nisi quod pedes effingit humanos; aures autem habet
noctuæ, et infra consuetam alvum aliam habet instar crumenæ, in qua
delitescunt catuli ejus tantisper, donec tuto prodire queant, et
absque parentis tutela cibatum quærere, nec unquam exeunt crumenam,
nisi cum sugunt. Portentosum hoc animal cum catulis tribus Sibiliam
delatum est; et ex Sibilia Illiberim, id est Granatam, in gratiam
regum, qui novis semper rebus oblectantur, p. 116, edit. 1532. In
Peter Martyr, De Rebus Oceanicis, dec. i. lib. 9, we find a longer
account of the monstrosum illud animal vulpino rostro,
cercopithecea cauda, verpertilioneis auribus, manibus humanius,
pedibus simiam æmulans; quod natos jam filios alio gestat quocunque
proficiscatur utero exteriore in modum magnæ crumenæ. This animal,
he says, lived some months in Spain, and was seen by him after its
death. Several species are natives of Guiana.

[1379] Tatus, quadrupes peregrina. The species figured in Gesner is
Dasypus novem cinctus. This animal, however, is mentioned by
Hernando d’Oviedo under the name Bardati.

[1380] Sunt et cynocephalorum diversa genera, nec unum genus
caudatorum. I think he knew the leading characteristics founded on
the tail, but did not attend accurately to subordinate
distinctions, though he knew them to exist. The three principal
Simian divisions were familiarly known in Europe not very long
after the time of Gesner, as we find by an old song of Elizabeth’s
time:--

The ape, the monkey, and baboon did meet
A breaking of their fast in Friday Street.
British Bibliographer, i. 342.

[1381] The Tapir is mentioned by Peter Martyr, the rest in Hernando.

|Belon.|

27. Less acquainted with books but with better opportunities of observing nature than Gesner, his contemporary Belon made greater accessions to zoology. Besides, his excellent travels in the Levant and Egypt, we have from him a history of fishes in Latin, printed in 1553, and translated by the author into French, with alterations and additions; and one of birds, published in French in 1555, written with great learning, though not without fabulous accounts, as was usual in the earlier period of natural history. Belon was perhaps the first, at least in modern times, who had glimpses of a great typical conformity in nature. In one of his works he places the skeletons of a man and a bird in apposition, in order to display their essential analogy. He introduced also many exotic plants into France. Every one knows, says a writer of the last century, that our gardens owe all their beauty to Belon.[1382] The same writer has satisfactorily cleared this eminent naturalist from the charge of plagiarism, to which credit had been hastily given.[1383] Belon may on the whole be placed by the side of Gesner.

[1382] Liron, Singularités Historiques, i. 456.

[1383] Id. p. 438. It had been suspected that the manuscripts of
Gilles, the author of a compilation from Ælian, who had himself
travelled in the east, fell into the hands of Belon who published
them as his own. Gesner has been thought to insinuate this; but
Liron is of opinion that Belon was not meant by him.

|Salviani and Rondelet’s Ichthyology.|

28. Salviani published in 1558 a history of fishes (Animalium Aquatilium Historia), with figures well executed, but by no means numerous. He borrows most of his materials from the ancients, and having frequently failed in identifying the species they describe, cannot be read without precaution.[1384] But Rondelet (De Piscibus Marinis, 1554), was far superior as an ichthyologist, in the judgment of Cuvier, to any of his contemporaries, both by the number of fishes he has known, and the accuracy of his figures, which exceed three hundred for fresh-water and marine species. His knowledge of those which inhabit the Mediterranean Sea was so extensive that little has been added since his time. “It is the work,” says the same great authority, “which has supplied almost everything which we find on that subject in Gesner, Aldrovandus, Willoughby, Artedi, and Linnæus; and even Lacepede has been obliged, in many instances, to depend on Rondelet.” The text, however, is far inferior to the figures, and is too much occupied with an attempt to fix the ancient names of the several species.[1385]

[1384] Biogr. Univ. (Cuvier.)

[1385] Biogr. Univ.

|Aldrovandus.|

29. The very little book of Dr. Caius on British Dogs, published in 1570, the whole of which I believe has been translated by Pennant in his British Zoology, is hardly worth mentioning; nor do I know that zoological literature has anything more to produce till almost the close of the century, when the first and second volumes of Aldrovandus’s vast natural history was published. These, as well as the third, which appeared in 1603, treat of birds; the fourth is on insects; and these alone were given to the world by the laborious author, a professor of natural history at Bologna. After his death in 1605, nine more folio volumes, embracing with various degrees of detail most other parts of natural history, were successively published by different editors. “We can only consider the works of Aldrovandus,” says Cuvier, “as an immense compilation without taste or genius; the very plan and materials being in a great measure borrowed from Gesner; and Buffon has had reason to say that it would be reduced to a tenth part of its bulk by striking out the useless and impertinent matter.”[1386] Buffon, however, which Cuvier might have gone on to say, praises the method of Aldrovandus and his fidelity of description, and even ranks his work above every other natural history.[1387] I am not acquainted with its contents; but according to Linnæus, Aldrovandus, or the editors of his posthumous volumes, added only a very few species of quadrupeds to those mentioned by Gesner, among which are the Zebra, the Jerboa, the Musk Rat of Russia, and the Manis or Scaly Anteater.[1388]

[1386] Id.

[1387] Hist. Naturelle, Premier Discours. The truth is that all
Buffon’s censures on Aldrovandus fall equally on Gesner, who is not
less accumulative of materials not properly bearing on natural
history, and not much less destitute of systematic order. The
remarks of Buffon on this waste of learning are very just, and
applicable to the works of the sixteenth century on almost every
subject as well as zoology.

[1388] Collections of natural history seem to have been formed by all
who applied themselves to the subject in the sixteenth century;
such as Cordus, Mathiolus, Mercati, Gesner, Agricola, Belon,
Rondelet, Ortelius, and many others. Hakluyt mentions the cabinets
of some English collectors from which he had derived assistance.
Beckmann’s Hist. of Inventions, ii. 57.

|Botany; Turner.|