## 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

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**these**Propofitions with more nicety , but per- haps none with more fuccinctness than I have ; efpeci- ally fince I alter'd nothing in the Number and Order of the Author's Propofitions ; nor prefum'd either to . take the Liberty of ... Página

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**these**Studies , nor feveral other things of the like Nature . But what I have bere employ'd my Labour and Study in for the Ufe of the ingenious Reader , I wholly Submit to his Cenfure and Judgment , to approve if useful , or reject if ... Página 3

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**these**trilateral figures , a right - angled tri- angle is that which hath one right - angle , as the triangle ABD . Fig . 5 . XXVII . An Amblygonium , or obtufe - angle triangle , that is which hath one angle obtufe ; as ABC . Fig . 5 ... Página 32

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**These**added tegether make 2Aq + 2Eq . Which was to be demonftrated . a 4. 2 . b cor . 4. 2 . € 4.2 . a 46. 1 . b 10. 1 . PROP . X. Fig . 53 . If a right - line A be divided into trvo equal parts , and ano- ther line be added in a right ... Página 33

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**these**are all equal ACq . ( a ) CDq + ADq . ( b ) CBq + 2CBD + BDq + ADq ; CBq + 2CBD + ( c ) ABq . Scholium . Hence , the fides of any obtufe - angled triangle ABC being known , the fegment BD intercepted betwixt the perpendicular AD ...### 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.