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 |
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Página 10
... PROP . X. Plate I. Fig . 20 . To bisect a right - line given AB . Upon the line given AB ( a ) erect an equilateral tri- angle ABC ; and ( 6 ) bisect the angle C with the right- line CD . That line shall also bisect the line given AB ...
... PROP . X. Plate I. Fig . 20 . To bisect a right - line given AB . Upon the line given AB ( a ) erect an equilateral tri- angle ABC ; and ( 6 ) bisect the angle C with the right- line CD . That line shall also bisect the line given AB ...
Página 14
... PROP . XXI . Plate I. Fig . 25 . 1 If from the utmost points of one fide BC , of a triangle ABC , two right - lines BD , CD , be drawn to any point within the triangle , then are both those two lines shorter than the two other fides of ...
... PROP . XXI . Plate I. Fig . 25 . 1 If from the utmost points of one fide BC , of a triangle ABC , two right - lines BD , CD , be drawn to any point within the triangle , then are both those two lines shorter than the two other fides of ...
Página 20
... PROP . XXXIII . Plate I. Fig . 7 . If two equal and parallel lines AB , CD , be joyned to- gether with two other right - lines , AC , BD , then are those lines also equal and parallel . Draw a line from C to B. Now because AB and CD are ...
... PROP . XXXIII . Plate I. Fig . 7 . If two equal and parallel lines AB , CD , be joyned to- gether with two other right - lines , AC , BD , then are those lines also equal and parallel . Draw a line from C to B. Now because AB and CD are ...
Página 22
... PROP . XXXVII . Plate I. Fig . 38 . Triangles , BCA , BCD , standing upon the same base BC , and between the same parallels BC , EF , are equal the one to the other . ( a ) Draw BE parallel to CA , ( a ) and CF parallel to BD . Then is ...
... PROP . XXXVII . Plate I. Fig . 38 . Triangles , BCA , BCD , standing upon the same base BC , and between the same parallels BC , EF , are equal the one to the other . ( a ) Draw BE parallel to CA , ( a ) and CF parallel to BD . Then is ...
Página 38
... PROP . V. Plate II . Fig . 7 . If two circles BAC , BDC , cut each other , they shall not have the fame center E. For otherwise the lines EB , EDA , drawn from E , the common center , would be DE ( a ) = EB ( a ) = EA ( b ) Which is ...
... PROP . V. Plate II . Fig . 7 . If two circles BAC , BDC , cut each other , they shall not have the fame center E. For otherwise the lines EB , EDA , drawn from E , the common center , would be DE ( a ) = EB ( a ) = EA ( b ) Which is ...
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Términos y frases comunes
ABC is given ABCD alfo alſo given altitude angle angle BAC arch baſe becauſe biſect circle commenfurable compounded Conftr conſequently Coroll cube demonstrated deſcribed diameter Dodecaedron drawn equal equilateral faid fame fide figure fince firſt folid Foraſmuch fore given angle given in kind given in magnitude given in poſition given Magnitude given ratio greater hath inſcribed leſs likewife Logarithm mean proportional meaſure medial multiplied parallel parallelogram pentagon perpendicular plane Plate prime priſms PROP pyramid rational-line rectangle refidual right-angles right-line AB right-line BC ſaid ſame ſay Schol Scholium ſecond ſeeing ſegment ſhall ſide ſolid ſpace ſphere ſquare ſquare number ſuperficies ſuppoſed theſe thoſe triangle ABC whence Wherefore 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.