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 15
... fide DG ( 6 ) = DF ( c ) = AC ; and let EG , and FG be joined . 1. Cafe . If EG falls above EF ; Because AB ( d ) ... fide of the other , either that fide which lyeth betwixt the equal angles , or that which is fubtended under one of ...
... fide DG ( 6 ) = DF ( c ) = AC ; and let EG , and FG be joined . 1. Cafe . If EG falls above EF ; Because AB ( d ) ... fide of the other , either that fide which lyeth betwixt the equal angles , or that which is fubtended under one of ...
Página 56
... fide of an Enneagon . But if AC , then is AB the fide of a square . And if A = 2 CAB will fub- tend the fixth part of the circumference , and likewife if A = 3C then will AB be the fide of an Octagon . PROP . XII . Plate III . Fig ...
... fide of an Enneagon . But if AC , then is AB the fide of a square . And if A = 2 CAB will fub- tend the fixth part of the circumference , and likewife if A = 3C then will AB be the fide of an Octagon . PROP . XII . Plate III . Fig ...
Página 121
... fide of the other ( B ) : and if the side of one Square A , measure the fide of another B , the square Aq shall likewise measure the square Bq . 1. Hyp . For Aq : AB ( a ) :: AB : Bq , therefore seeing by the hypothefis Aq measures ...
... fide of the other ( B ) : and if the side of one Square A , measure the fide of another B , the square Aq shall likewise measure the square Bq . 1. Hyp . For Aq : AB ( a ) :: AB : Bq , therefore seeing by the hypothefis Aq measures ...
Página 122
... fide of one A measure the fide of the other B : And if A the fide of cube Ac does not mea- fure B the fide of the other Bc , neither shall the cube Ac mea- fure the cube Bc . one 1. Hyp . Let A measure B ; ( a ) then Ac - hall measure ...
... fide of one A measure the fide of the other B : And if A the fide of cube Ac does not mea- fure B the fide of the other Bc , neither shall the cube Ac mea- fure the cube Bc . one 1. Hyp . Let A measure B ; ( a ) then Ac - hall measure ...
Página 232
... fide of an Hexagon BE , and the fide of a Decagon AB both described in the fame circle ABC , be added together , the whole right - line AE is cut according to extreme and . mean proportion ( AE : BE :: BE : AB . ) and the greater ...
... fide of an Hexagon BE , and the fide of a Decagon AB both described in the fame circle ABC , be added together , the whole right - line AE is cut according to extreme and . mean proportion ( AE : BE :: BE : AB . ) and the greater ...
Otras ediciones - Ver todas
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.