## 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 |

### From inside the book

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**axes**perpendicular to each other , and for their respective parameters the side of the given cube and the double of that side : then the two ordinates , drawn to the point of intersection of the two curves , are the two mean mean ... Page 30

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**axis**one of the assymptotes of the equilateral hyperbola ; and the power of the hyperbola is the product of the side of the given cube by the double of that side . Lastly the ordinates of the two curves , drawn to the point of ... Page 33

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**axis**, and the distance of the two movable points , are deter- mined by the conditions of whichever of the two problems is to be solved . Newton , in an appendix to his Arithmetic , passes the highest encomium on the invention of ... Page 40

... of the sphere is two thirds that of the cylinder : & c . The treatise on Conoids contains several properties of solids produced by the revolution of the conic sections round round their

... of the sphere is two thirds that of the cylinder : & c . The treatise on Conoids contains several properties of solids produced by the revolution of the conic sections round round their

**axes**. with one another ; and determines 40. Page 41

Charles Bossut. round their

Charles Bossut. round their

**axes**. with one another ; and determines their ratios to the cylinder and the cone of the same base and altitude : he also demonstrates , for example , that the solidity of the paraboloid is only half that of ...### 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...