The Elements of Euclid: 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 Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 Seiten |
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Seite 275
... cylinder to the cylinder , because b * 15 . 5 . the cylinders are triple of the cone , each to each . Therefore , c 10. 12 . as the circle ABCD to the circle EFGH , so are the cylinders up- on them of the same altitude . Wherefore ...
... cylinder to the cylinder , because b * 15 . 5 . the cylinders are triple of the cone , each to each . Therefore , c 10. 12 . as the circle ABCD to the circle EFGH , so are the cylinders up- on them of the same altitude . Wherefore ...
Seite 279
... cylinder to the cylinder ; for every cone is the b 15. 5 . third part of the cylinder upon the same base , and of the same altitude : therefore also the cylinder has to the cylinder the tri- plicate ratio of that which AC has to EG ...
... cylinder to the cylinder ; for every cone is the b 15. 5 . third part of the cylinder upon the same base , and of the same altitude : therefore also the cylinder has to the cylinder the tri- plicate ratio of that which AC has to EG ...
Seite 280
... cylinder AD into the cylinders AH , GD ; for they are the same which would be described by the revolution of the parallelograms AK , GF , about the straight lines EK , KF : and it is to be shown , that the cylinder AH is to the cylinder ...
... cylinder AD into the cylinders AH , GD ; for they are the same which would be described by the revolution of the parallelograms AK , GF , about the straight lines EK , KF : and it is to be shown , that the cylinder AH is to the cylinder ...
Seite 281
... cylinder BG to the cylinder GD . fore , if a cylinder , & c . Q. E. D. PROP . XIV . THEOR . CONES and cylinders upon equal bases are to one another as their altitudes . Let the cylinders EB , FD be upon the equal bases AB , CD : as the ...
... cylinder BG to the cylinder GD . fore , if a cylinder , & c . Q. E. D. PROP . XIV . THEOR . CONES and cylinders upon equal bases are to one another as their altitudes . Let the cylinders EB , FD be upon the equal bases AB , CD : as the ...
Seite 282
... cylinder AX is equal to the cylinder EO , as AX is to the cylinder ES , so cis the cylinder EO to the same ES . But as the cylinder AX to the cylinder ES , so a is the base ABCD to the base EFGH ; for the cylinders AX , ES are of the ...
... cylinder AX is equal to the cylinder EO , as AX is to the cylinder ES , so cis the cylinder EO to the same ES . But as the cylinder AX to the cylinder ES , so a is the base ABCD to the base EFGH ; for the cylinders AX , ES are of the ...
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram perpendicular point F polygon prisms proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar sine solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
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Seite 30 - Any two sides of a triangle are together greater than the third side.
Seite 64 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Seite 30 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...
Seite 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite 165 - 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.
Seite 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Seite 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Seite 39 - 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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Seite 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.