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
... fegment ( or part ) common to them both . 11. Two right - lines meeting in the fame point , if they be both produced , they shall neceffarily cut one another in that point . 12. All right - angles are equal the one to the other . 13. If ...
... fegment ( or part ) common to them both . 11. Two right - lines meeting in the fame point , if they be both produced , they shall neceffarily cut one another in that point . 12. All right - angles are equal the one to the other . 13. If ...
Página 27
... fegments as you please ; the rectangle comprehended under the two whole right - lines AB , AF , shall be equal to all the rectangles contained under the whole line AF , and the several fegments , AD , DE , EB . ( a ) Set AF ...
... fegments as you please ; the rectangle comprehended under the two whole right - lines AB , AF , shall be equal to all the rectangles contained under the whole line AF , and the several fegments , AD , DE , EB . ( a ) Set AF ...
Página 29
... fegment E. 1 I fay ZE = AE + Eq . ( a ) For EZ = EA + Eq . PROP . IV . Fig . 50 . If a right - line Z be cut any wife into two parts , the Square described on the whole line Z , is equal to the squares described on the fegments A , E ...
... fegment E. 1 I fay ZE = AE + Eq . ( a ) For EZ = EA + Eq . PROP . IV . Fig . 50 . If a right - line Z be cut any wife into two parts , the Square described on the whole line Z , is equal to the squares described on the fegments A , E ...
Página 31
... fegment E , to- gether with the square made of the other fegment A. I fay , that Zq + Eq = 2ZE + Aq . For Zq ( a ) = Aq + Eq - 1-2AE , and 2 ZE ( 6 ) = 2 Eq + 2AE . Which was to be demonstrated . Coroll . Hence it follows , that the ...
... fegment E , to- gether with the square made of the other fegment A. I fay , that Zq + Eq = 2ZE + Aq . For Zq ( a ) = Aq + Eq - 1-2AE , and 2 ZE ( 6 ) = 2 Eq + 2AE . Which was to be demonstrated . Coroll . Hence it follows , that the ...
Página 35
... fegment of a circle ( BPC ) is a figure contained under a right - line BC , and a portion of the circumfe- rence of a circle BPC . VI . An angle of a fegment CBP , is that angle which is contained under a right - line BC , and the ...
... fegment of a circle ( BPC ) is a figure contained under a right - line BC , and a portion of the circumfe- rence of a circle BPC . VI . An angle of a fegment CBP , is that angle which is contained under a right - line BC , and the ...
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.