## 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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**Parallel**, or equi - diftant right - lines are fuch , which being in the fame fuperficies , if infinitely produced , would never meet as AD and BC . Fig . 11 . A 2 XXXV , XXXV . A Parallelogram is a quadrilateral figure , whofe ... Página 4

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**parallel**, or equi - diftant ; as ABCD . Plate I. Fig . 7 . XXXVI . In a Parallelogram AGEL , Fig . 9. when a diameter AE , and two lines BK , CF ,**parallel**to the fides , cutting the diameter in one and the fame point D , are drawn ... Página 16

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**parallel**. If AB , CD be faid not to be**parallel**, produce them till they meet in O , which being fuppofed , the outward angle AF will be ( a ) greater than the inward angle De E , to which it was equal by Hypothefis . Which things are ... Página 17

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**parallel**, Which was to he demonfirated . PRO P. XXIX . Plate I. Fig . 33 . If a right - line EF falls upon two**parallels**, AB , CD , it will make both the alternate angles DHG , AGH , equal each to the other , and the outward angle BGE ... Página 18

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**parallel**to BA . Then is the angle A ( b ) ACE , and the angle B ( b ) —ECD . Therefore A + B ( c ) ≈ACE + ECD ( d ) = ACD . Which was to be demonftrated . I affirm ACD + ACB ( e ) two right - angles ; ( f ) therefore A + B + ACB two ...### 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.