A General History of Mathematics from the Earliest Times to the Middle of the Eighteenth Century. Tr. from the French of John [!] Bossut ... To which is Affixed a Chronological Table of the Most Eminent MathematiciansJ. Johnson, 1803 - 540 pages |
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Page 220
... into series of which each term is a monomial . The author's dispute with Pascal on the subject of the cycloid shall be mentioned hereafter . Wallis was a profound analyst : analyst to him we are indebted for the notation of 220.
... into series of which each term is a monomial . The author's dispute with Pascal on the subject of the cycloid shall be mentioned hereafter . Wallis was a profound analyst : analyst to him we are indebted for the notation of 220.
Page 232
... cycloid , a curve that had become cele- brated by it's numerous and singular properties . He determined the area of this curve , and the solids it generated by turning round it's base or it's axis : he likewise found the centre of ...
... cycloid , a curve that had become cele- brated by it's numerous and singular properties . He determined the area of this curve , and the solids it generated by turning round it's base or it's axis : he likewise found the centre of ...
Page 233
... cycloid , which , being a mechanical curve , required methods different from those already employed for drawing tangents to geometrical curves . Roberval had framed a general method for tan- gents , which was applicable to geometrical ...
... cycloid , which , being a mechanical curve , required methods different from those already employed for drawing tangents to geometrical curves . Roberval had framed a general method for tan- gents , which was applicable to geometrical ...
Page 234
... cycloid he mortally offended Torricelli . This illustrious italian geometer having published solutions of these pro- blems , as of his own invention , in 1644 , Roberval claimed them ; maintaining that they were funda- mentally the same ...
... cycloid he mortally offended Torricelli . This illustrious italian geometer having published solutions of these pro- blems , as of his own invention , in 1644 , Roberval claimed them ; maintaining that they were funda- mentally the same ...
Page 237
... cycloid began to be a little forgotten by ge- ometricians , when Pascal brought it forward again in 1658 , by proposing new problems relating to this curve , and offering prizes to those who should solve them . The total area of the cycloid ...
... cycloid began to be a little forgotten by ge- ometricians , when Pascal brought it forward again in 1658 , by proposing new problems relating to this curve , and offering prizes to those who should solve them . The total area of the cycloid ...
Other editions - View all
A General History of Mathematics From the Earliest Times to the Middle of ... John Bonnycastle,Charles Bossut No preview available - 2023 |
A General History of Mathematics from the Earliest Times to the Middle of ... John Bonnycastle,Charles Bossut No preview available - 2015 |
A General History of Mathematics from the Earliest Times to the Middle of ... Charles Bossut No preview available - 2019 |
Common terms and phrases
Academy afterward algebra Almagest analysis of infinites ancient angle appeared arabs Archimedes arithmetic astro astronomy axis blems bodies calculation Cartes celebrated celestial centre of gravity century CHAP circle Clairaut comets conic sections considered curve cycloid d'Alembert Daniel Bernoulli degree demonstrated determined differential calculus discovery Earth ecliptic ellipsis employed equal equilibrium errour Euler fluid formulæ Galileo gave genius geometricians geometry given glass Hipparchus Huygens invention isochronous curve James Bernoulli John Bernoulli Jupiter known laws Leibnitz length likewise lunar marquis de l'Hopital mathematicians mathematics maxima and minima means mechanics meridian method of fluxions Moon motion nature Newton Nicholas Bernoulli object observations occasion optics orbit particular planets principle problem progress proposed Ptolemy published quadratures quantity ratio rays refraction resolved respect revolution round simple solar solid solution spherical spheroid square stars supposed tangents telescope theory tion treatise truth velocity
Popular passages
Page 61 - ... any account of them in writing. For he considered all attention to Mechanics, and every art that ministers to common uses, as mean and sordid, and placed his whole delight in those intellectual speculations, which, without any relation to the necessities of life, have an intrinsic excellence arising from truth and demonstration only.
Page 61 - ... he did not think the inventing of them an object worthy of his serious studies, but only reckoned them among the amusements of geometry. Nor had he gone so far, but at the pressing instances of...
Page 163 - In the dial-plate there were twelve small windows, corresponding with the divisions of the hours. The hours were indicated by the opening of the windows, which let out little metallic balls, which struck the hour by falling upon a brazen bell.
Page 138 - AVhcu a summons is sent to me I will take this stone, and, placing myself in the sun, I will, though at a distance, melt all the writing of the summons.
Page 30 - ... to have led to the discoveries of other geometrical properties, as the conchoid of Nicomedes, the cissoid of Diocles, and the quadratrix of Dinostratus. This latter geometrician was the follower and friend of Plato, whose devotion to the science of geometry was such that he caused it to be inscribed over the door of his school, ' Let no one enter here who is ignorant of geometry.
Page 61 - Yet Archimedes had such a depth of understanding, such a dignity of sentiment, and so copious a fund of mathematical knowledge, that, though in the invention of these machines he gained the reputation of a man endowed with divine rather than human knowledge, yet he did not vouchsafe to leave any account of them in writing.
Page 65 - The reason is, all bodies lose some of their weight in a fluid, and the weight which a body loses in a fluid, is to its whole weight, as the specific gravity of the fluid is to that of the body.
Page 95 - Sunt Aries, Taurus, Gemini, Cancer. Leo, Virgo, Libraque, Scorpius, Arcitenens, Caper, Amphora, Pisces.
Page 297 - This is the same as saying that when a ray of light passes out of one medium into another, the...
Page 248 - Huyghens demonstrated that the velocity of a body descending down any curve, is the same at every instant, in the direction of the tangent, as it would have...