## 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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**fide**of a Rectangle into another . The fame is denoted by the Conjunction of Letters ; as AB = AxB . Continued Proportion . The Side or Root of a Square , or Cube , & c . ✓ Q & q A Square . C & C A Cube . The Ratio of a fquare Number ... Página 2

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**fide**thereof , CGA , CGB , equal one to the other , then both those equal angles are right - angles ; and the right - line CG , which ftandeth on the other , is termed a Perpendicular to that ( AB ) where- on it ftandeth . Note , When ... Página 5

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**fide**, GFE , FEG , lefs than two right - angles , those two right - lines produced fhall meet on that**fide**where the angles are lefs than two right - angles . 14. Two right - lines do not contain a space . 15. If to equal things you add ... Página 7

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**fide**( that is BA - ED , and AC = DF ) and have the angel A equal to the angle D contained under the equal right - lines ; they shall have the bafe BC equal to the bafe EF ; and the triangle BAC shall be equal to the triangle EDF ; and ... Página 8

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**fide**, AC is common , and the angle BAC ( d ) ACB , the triangles FAC , ACB ( e ) shall be equal the one to the other , a part to the whole , ( f ) Which is impossible . Caroll . Hence , every equiangular triangle is alfo equilateral ...### 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.