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 5
... shall meet on that fide where the angles are less than two right - angles . 14. Two right - lines do not contain a space . 15. If to equal things you add things unequal , the excess of the wholes shall be equal to the excess of the ...
... shall meet on that fide where the angles are less than two right - angles . 14. Two right - lines do not contain a space . 15. If to equal things you add things unequal , the excess of the wholes shall be equal to the excess of the ...
Página 7
... shall cut off DE ( b ) = BD ( c ) = A ( d ) = DE . Which was to be done . PROP . IV . Fig . 15 , and 16 . If two ... shall have the base BC equal to the base EF ; and the triangle BAC shall be equal to the triangle EDF ; and the ...
... shall cut off DE ( b ) = BD ( c ) = A ( d ) = DE . Which was to be done . PROP . IV . Fig . 15 , and 16 . If two ... shall have the base BC equal to the base EF ; and the triangle BAC shall be equal to the triangle EDF ; and the ...
Página 11
... shall make one ftrait - line . If you deny it , let AG , GF make one right - line ; then shall the angle CGA + CGF ( a ) two right angles ( 6 ) = CGA + CGB . Which is ( c ) abfurd . PROP . XV . Fig . 21 . If two right - lines AB , CD ...
... shall make one ftrait - line . If you deny it , let AG , GF make one right - line ; then shall the angle CGA + CGF ( a ) two right angles ( 6 ) = CGA + CGB . Which is ( c ) abfurd . PROP . XV . Fig . 21 . If two right - lines AB , CD ...
Página 13
... shall fall on that side the acute angle is of . For if AC , drawn on the side of the obtufe - angle , be a perpendicular , then in the triangle AEC , shall the angles AEC + ACE be greater than two right - angles . * Which is contrary to ...
... shall fall on that side the acute angle is of . For if AC , drawn on the side of the obtufe - angle , be a perpendicular , then in the triangle AEC , shall the angles AEC + ACE be greater than two right - angles . * Which is contrary to ...
Página 14
... shall the angle D be equal to ACD ; ( c ) therefore is the whole angle BCDED ; ( d ) therefore BD ( e ) ( BA + AC ) BC . Which was to be demonstrated . PROP . XXI . Plate I. Fig . 25 . 1 If from the utmost points of one fide BC , of a ...
... shall the angle D be equal to ACD ; ( c ) therefore is the whole angle BCDED ; ( d ) therefore BD ( e ) ( BA + AC ) BC . Which was to be demonstrated . PROP . XXI . Plate I. Fig . 25 . 1 If from the utmost points of one fide BC , of a ...
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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.