The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner CorrectedDesilver, 1829 - 516 páginas |
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Página 196
... cylinder are the circles described by the two re- volving opposite sides of the parallelogram . XXIV . Similar cones and cylinders are those which have their axes and the diameters of their bases proportionals . XXV . A cube is a solid ...
... cylinder are the circles described by the two re- volving opposite sides of the parallelogram . XXIV . Similar cones and cylinders are those which have their axes and the diameters of their bases proportionals . XXV . A cube is a solid ...
Página 267
... cylinder which has the same base , and is of an equal altitude with it . Let a cone have the same base with a cylinder , viz . the circle ABCD , and the same altitude . The cone is the third part of the cylinder ; that is , the cylinder ...
... cylinder which has the same base , and is of an equal altitude with it . Let a cone have the same base with a cylinder , viz . the circle ABCD , and the same altitude . The cone is the third part of the cylinder ; that is , the cylinder ...
Página 268
... cylinder ; this prism is greater than half of the cylinder : be- cause if a square be described about the circle , and a prism erected upon the square , of the same altitude with the cylinder , the inscribed square is half of that ...
... cylinder ; this prism is greater than half of the cylinder : be- cause if a square be described about the circle , and a prism erected upon the square , of the same altitude with the cylinder , the inscribed square is half of that ...
Página 269
... cylinder , that is , the prism of which the base is the polygon AEBFCGDH , and of which the altitude is the same with that of the cylinder , is greater than the triple of the cone : but this prism is triple ( 1. Cor . 7. 12. ) of the ...
... cylinder , that is , the prism of which the base is the polygon AEBFCGDH , and of which the altitude is the same with that of the cylinder , is greater than the triple of the cone : but this prism is triple ( 1. Cor . 7. 12. ) of the ...
Página 270
... cylinder . But this pyramid is the third part of the E prism upon the same base AEBFCGDH , and of the same altitude with the cy- linder . Therefore this prism is great- er than the cylinder of which the base is the circle ABCD . But it ...
... cylinder . But this pyramid is the third part of the E prism upon the same base AEBFCGDH , and of the same altitude with the cy- linder . Therefore this prism is great- er than the cylinder of which the base is the circle ABCD . But it ...
Otras ediciones - Ver todas
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Sin vista previa disponible - 2018 |
Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 81 - The angles in the same segment of a circle are equal to one another.
Página 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.
Página 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Página 24 - Any two sides of a triangle are together greater than the third side.