Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated: with Archimede's Theorems of the Sphere and Cylinder, Investigated by the Method of Indivisibles. Also, Euclide's Data, and A Brief Treatise [added by Flussas] of Regular SolidsW. and J. Mount, 1751 - 384 páginas |
Dentro del libro
Resultados 1-5 de 39
Página 28
... given are both divided into how many parts foever , one whole multiplied into the other hall bring out the fame ... kind , arifing from the comparing of lines multiplied into themselves ( which you may find done to your hand in ...
... given are both divided into how many parts foever , one whole multiplied into the other hall bring out the fame ... kind , arifing from the comparing of lines multiplied into themselves ( which you may find done to your hand in ...
Página 82
... kind , which is against the Hypothefis . e 9.5 . 5. 1 . f cor . 13. 1 . a hyp . b 12. ax . © 32. 1. & 4. 6 . PRO P ... given AB to cut off any part required , as one third ( AG . ) From the point A draw an infinite line AC any wise ...
... kind , which is against the Hypothefis . e 9.5 . 5. 1 . f cor . 13. 1 . a hyp . b 12. ax . © 32. 1. & 4. 6 . PRO P ... given AB to cut off any part required , as one third ( AG . ) From the point A draw an infinite line AC any wise ...
Página 144
... kind . Axioms . 1. A magnitude measuring how many magnitudes for ever , does ... given , if from the greater AB there be taken away more than half ( AH ) and ... given C. ( a ) Take C fo often , till its multiple does fomewhat ex ...
... kind . Axioms . 1. A magnitude measuring how many magnitudes for ever , does ... given , if from the greater AB there be taken away more than half ( AH ) and ... given C. ( a ) Take C fo often , till its multiple does fomewhat ex ...
Página 251
... given in Magnitude . II . A Ratio is faid to be given , when we or one equal to it . can find it , III . Rectiline - figures , whofe angles are given , and alfe the ratio of the fides to one another , are said to be given in Species or Kind ...
... given in Magnitude . II . A Ratio is faid to be given , when we or one equal to it . can find it , III . Rectiline - figures , whofe angles are given , and alfe the ratio of the fides to one another , are said to be given in Species or Kind ...
Página 277
... given ratio to the fame EF ; and if through the extremity G of the added line EG , there be drawn a right - line HK ... kind . Conftr . For , let there be expofed the right - line DG given in pofition , ending in the point D ; but ...
... given ratio to the fame EF ; and if through the extremity G of the added line EG , there be drawn a right - line HK ... kind . Conftr . For , let there be expofed the right - line DG given in pofition , ending in the point D ; but ...
Otras ediciones - Ver todas
Términos y frases comunes
ABC is given ABCD alfo given alſo altitude angle BAC bafes baſe becauſe circle commenfurable confequently Conftr Coroll cube defcribed demonftrated diameter Dodecaedron drawn equal equilateral faid fame fecond feeing fegment fhall fide figure fince firft firſt folid angle Forafmuch fore fquare fuperficies fuppofe given angle given in kind given in magnitude given in pofition given Magnitude given ratio greater hath Hypothefis Icofaedron infcribed lefs likewife Logarithm mean proportional meaſure medial multiplied oppofite parallel parallelogram pentagon perpendicular plane Plate prifms PROP pyramid rectangle refidual refidual-line right-angles right-line AB right-line BC Schol Scholium ſhall ſpace Space AC ſphere ſquare theſe thofe thoſe triangle ABC whence Wherefore whofe whole whoſe
Pasajes populares
Página 18 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 281 - ... which, when produced, the perpendicular falls, and the straight line intercepted, without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle ACB, and from the point A let AD be drawn...
Página 2 - XV. A Circle is a plain figure contained under one line, which is called a circumference ; unto which all lines, drawn from one point within the figure, and falling upon the circumference thereof, are equal the one to the other. XVI. And that point is called the center of the circle. XVII. A Diameter of a circle is a right-line drawn thro' the center thereof, and ending at the circumference on either fide, dividing the circle into two equal parts.
Página 95 - An EVEN NUMBER is that which can be divided into two equal whole numbers.
Página 381 - Rule. Multiply the Logarithm of the given number by the Index of the proposed power, and the product will be the Logarithm, whose natural number is the power required.
Página 197 - ... than the other side, an obtuse-angled ; and if greater, an acute-angled cone. XIX. The axis of a cone is the fixed straight line about which the triangle revolves. XX. The base of a cone is the circle described by that side containing the right angle, which revolves. XXI. A cylinder is a solid figure described by the revolution of a rightangled parallelogram about one of its sides which remains fixed.
Página 196 - ... are •not in the fame Superficies: Or, a folid Angle is that which is contained under more than two plane Angles which are not in the fame Superficies, but being all at one Point. XII. A Pyramid is a folid Figure comprehended under divers Planes fet upon one Plane, and put together at one Point. ' «. XIII. A Prifm is a folid Figure contained under Planes, whereof the two oppofite are equal, fimilar, and parallel, and the others Parallelograms.
Página 353 - To divide one number by another.* Subtract the logarithm of the divisor from the logarithm of the dividend, and the remainder will be the logarithm of the quotient.
Página 2 - ... parts. XVIII. A Semicircle is a figure which is contained under the diameter and that part of the circumference which is cut off by the diameter. In the circle EABCD, E is the center, AC the diameter > ABC the femi circle.
Página 51 - ... touch the circumference of the circle. IV A right-lined figure is faid to be defcribed about a circle, when all the fides of the figure which is circumfcribed touch the periphery of the circle V.