## Tracts on mathematical and philosophical subjects: comprising among numerous important articles, the theory of bridges, with several plans of recent improvement; also the results of numerous experiments on the force of gunpowder, with applications to the modern practice of artillery ... |

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2d term Albert Girard algebra altitude angles Arabians arithmetic attraction axis ball binomial Cardan centre of gravity centre of oscillation Chap chord coefficient column compound computed contains cube root cubic equations denote Descartes diameter Diophantus distance divided divisor equa equal equation x3 extraction feet former geometrical given gives greater greatest root Gun n hence hyperbola imaginary roots infinite series Jebr least root length less letters manner means measured method multiply namely nearly negative notation observed pendulum Point struck Pole Vert positive roots powers published quadratic equations quotient Radii radius ratio real root recoil reduced rule Shai side signs sines square root subtract surds tangents tape Tartalea Theodolite theorem three roots tion triangles unknown quantity velocity vertical vibration Vieta weight whole Z's Bearings Diff

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Page 310 - ... of two or three times the weight of its natural ball, or round shot: and thus a small ship might discharge shot as heavy as those of the greatest now made use of.

Page 143 - Venice, from 1791 to 1794, 17 vols. ALGEBRA is a general method of resolving mathematical problems by means of equations, or it is a method of performing the calculations of all sorts of quantities by means of general signs or characters. Some authors define algebra as the art of resolving mathematical problems ; but this is the idea of analysis, or the analytic art in general, rather than of algebra, which is only one species of it. In the application of algebra to the resolution of problems, we...

Page 178 - ... the long-expected hour was passed. In short, the father, thus disappointed, said to his unfortunate daughter, ' I will write a book of your name, which shall remain to the latest times, — for a good name is a second life, and the groundwork of eternal existence.

Page 145 - ... and quantities, both known and unknown, by their proper characters, arranged in an equation, or several equations, if necessary, and treating the unknown quantity as if it were a known one ; this forms the composition. Then the resolution or analytic part is the disentangling the unknown quantity from the several others with which it is connected, so as to retain it alone on one side of the equation, while all the known quantities are collected on the other side, thus obtaining the value of the...

Page 310 - ... discharged with the same charge of powder, would be increased in the ratio of the square root of the weight of the shot...

Page 178 - But as the intended arrangement was not according to destiny, it happened that the girl, from a curiosity natural to children, looked into the cup to observe the water coming in at the hole ; when by chance a pearl separated from her bridal dress, fell into the cup, and, rolling down to the hole, stopped the influx of the water.

Page 309 - And first, it is made evident by the experiments in 1775, that powder fires almost instantaneously, seeing that nearly the whole of the charge fires, though the time be much diminished. ' (2.) The velocities communicated to shot of the same weight, with different quantities of powder, are nearly in the sub'duplicate ratio of those quantities. A very small variation, in defect, taking place when the quantities of powder become great. ' (3.) And when shot of different weights are fired with the same...

Page 245 - And to avoide the tediouse repetition of these woordes : is equalle to : I will sette as I doe often in woorke use, a paire of paralleles, or Gemowe lines of one lengthe, thus : =, bicause noe 2 thynges can be more equalle.

Page 177 - He then opened the volume, and read as follows : " It is said that the composing of Lilawati was occasioned by the following circumstance. Lilawati was the name of the author's daughter, concerning whom it appeared, from the qualities of the Ascendant at her birth, that she was destined to pass her life unmarried, and to remain without children. The father ascertained a lucky hour for contracting her in marriage, that she might be firmly connected, and have children. It is said that, when that hour...

Page 228 - I swear to you, by God's holy Gospels, and as a true man of honour, not only never to publish your discoveries, if you teach me them, but I also promise you, and I pledge my faith as a true Christian, to note them down in code, so that after my death no one will be able to understand them.