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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 28.
Σελίδα 21
... altitude BA drawn into the base BC . For the area of the rectangle AC = parallelogram EBCF , is made by the drawing of BA into BC , therefore , & c . PROP . XXXVI . Fig 37 . Parallelograms BCDA , GHFE , standing upon coual bafes BC , GH ...
... altitude BA drawn into the base BC . For the area of the rectangle AC = parallelogram EBCF , is made by the drawing of BA into BC , therefore , & c . PROP . XXXVI . Fig 37 . Parallelograms BCDA , GHFE , standing upon coual bafes BC , GH ...
Σελίδα 23
... altitude drawn into the base , or half the base drawn into the altitude ; thus , if the base BC be 8 , and the altitude 7 , then is the area of the triangle BCE 28 . PROP . XLII . Plate I. Fig . 41 . To make a Pgr . ECGF equal to a ...
... altitude drawn into the base , or half the base drawn into the altitude ; thus , if the base BC be 8 , and the altitude 7 , then is the area of the triangle BCE 28 . PROP . XLII . Plate I. Fig . 41 . To make a Pgr . ECGF equal to a ...
Σελίδα 78
... altitude of any figure ABC , is a perpendicu- lar line AG , drawn from the top A , to the base BC . V. A ratio is said to be compounded of ratio's , when the quantities of the ratio's , being multiplied into one another , produce a ...
... altitude of any figure ABC , is a perpendicu- lar line AG , drawn from the top A , to the base BC . V. A ratio is said to be compounded of ratio's , when the quantities of the ratio's , being multiplied into one another , produce a ...
Σελίδα 79
... altitudes , AI , DK . 1 a 3. I. b 38. 1 . c fch , 38.1 . d 6. def . 5 . e 41. 1. & 15.5 . a 3. 1 . b 7.5 . 7 :: с 1. 6 . ( a ) Take IL = CB , and KM EF ; and join LA , LG , MD , MH , then it is evident , that the triangle ABC : DEF ...
... altitudes , AI , DK . 1 a 3. I. b 38. 1 . c fch , 38.1 . d 6. def . 5 . e 41. 1. & 15.5 . a 3. 1 . b 7.5 . 7 :: с 1. 6 . ( a ) Take IL = CB , and KM EF ; and join LA , LG , MD , MH , then it is evident , that the triangle ABC : DEF ...
Σελίδα 90
... altitude to altitude . After the like manner you may argue in triangles . 3. From hence is apparent how to give the proportion of triangles and parallelograms . Let there be two Pgrs . X and Z , whose bases are AC , CB , and altitudes ...
... altitude to altitude . After the like manner you may argue in triangles . 3. From hence is apparent how to give the proportion of triangles and parallelograms . Let there be two Pgrs . X and Z , whose bases are AC , CB , and altitudes ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 95 - An EVEN NUMBER is that which can be divided into two equal whole numbers.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.