## 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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abutments angle Answer arithmetical means binomial binomial theorem Blackfriars bridge breadth Briggs calculation centre chords circle coefficients column computed consequently construction converging converging series Corol cosine cube curve degrees denote diameter diverging series divided equal equation equilibrio expression extrados feet fluxion force former formula fraction frame gives greater Hence horizontal thrust hyperbola infinite series iron bridge joints less loga logarithms London bridge manner method metical multinomial theorem multiplied namely Napier natural numbers nearer nearly oblique perpendicular pier places of figures powers pressure prop properties proportion proposed proposition quadrant quadratic equation quantity quotient radius ratio ribs rithms river river Thames secants side sines soffit span sphere square subtraction successive sums supposed tangent tangents and secants theorem thickness tide tion TRAct triangle trigonometry velocity versed sine vertex voussoirs wedge weight whole

### Popular passages

Page 325 - Napier lord of Markinston, hath set my head and hands at work with his new and admirable logarithms. I hope to see him this summer, if it please God ; for I never saw a book which pleased me better, and made me more wonder.

Page 318 - ... by addition and subtraction, division by two, or division by three : which secret invention, being (as all other good things are) so much the better as it shall be the more common ; I thought good heretofore to set forth in Latine for the publique use of mathematicians.

Page 364 - Kepler's work, however, it may not be improper in this place to take notice of an erroneous property laid down by him in the appendix to the 27th prop...

Page 318 - ... Seeing there is nothing (right well-beloved Students of the Mathematics) that is so troublesome to mathematical practice, nor that doth more molest and hinder calculators, than the multiplications, divisions, square and cubical extractions of great numbers, which besides the tedious expense of time are for the most part subject to many slippery errors, I began therefore to consider in my mind by what certain and ready art I might remove those hindrances.

Page iv - ... +ex4 -(-,&c., when it converges very slowly ; the investigation of a general rule for extracting roots ; new methods for the roots of equations ; a demonstration of the truth of the binomial theorem in the case of fractional exponents; curious properties of the common section of a sphere and cone; the geometrical division of circles and ellipses into any number of parts that shall be equal both in area and in perimeter ; and, lastly, a copious and instructive tract relating to experiments and...

Page 429 - Now thefe rativncula are fb to be underflood as in a continued Scale of Proportionals infinite in Number between the two terms of the ratio, . which infinite Number of mean Proportionals is to that infinite Number of the like and equal...

Page 429 - ... as in a continued scale of proportionals, infinite in number, between the two terms of the ratio ; which infinite number of mean proportionals is to that infinite number of the like and equal...

Page 310 - tis said) to save the tedious multiplication and division in astronomical calculations. Neper being solicitous to know farther of him concerning this matter, he could give no other account of it, than that it was by proportionable numbers. Which hint Neper taking, he desired him at his return to call upon him again. Craig, after some weeks had passed, did so, and Neper then shewed him a rude draught of that he called ' Canon Mirabilis Logarithmorum.

Page 379 - The 10th chapter is employed in teaching how to find the logarithms of fractions, namely by subtracting the logarithm of the denominator from that of the numerator, then the logarithm of the fraction is the remainder...

Page 417 - ... practice of navigation, by Henry Bond, who mentions this property in an edition of Norwood's Epitome of Navigation, printed about 1645; and he again treats of it more fully in an edition of Gunter's works, printed in 1653, where he teaches, from this property, to resolve all the cases of Mercator's sailing by the logarithmic tangents, independent of the table of meridional parts. This analogy had only been found to be nearly true by trials, but not demonstrated to be a mathematical property....