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 páginas |
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Página 231
... altitude , the insisting straight lines of which are not terminated in the same straight lines in the plane opposite to the base , are equal to one another . Let the parallelepipeds CM , CN be upon the same base AB , and of the same ...
... altitude , the insisting straight lines of which are not terminated in the same straight lines in the plane opposite to the base , are equal to one another . Let the parallelepipeds CM , CN be upon the same base AB , and of the same ...
Página 232
... altitude , are equal to one another . Let the solid parallelepipeds AE , CF be upon equal bases AB , CD , and be of the same altitude ; the solid AE is equal to the so- lid CF. First , Let the insisting straight lines be at right angles ...
... altitude , are equal to one another . Let the solid parallelepipeds AE , CF be upon equal bases AB , CD , and be of the same altitude ; the solid AE is equal to the so- lid CF. First , Let the insisting straight lines be at right angles ...
Página 233
... altitude , and let their insisting straight lines be at right angles to the bases ; and place the bases SB , CD in the same plane , so that CL , LB be in a straight line ; and let the angles SLB , CLD be unequal ; the solid SE is also ...
... altitude , and let their insisting straight lines be at right angles to the bases ; and place the bases SB , CD in the same plane , so that CL , LB be in a straight line ; and let the angles SLB , CLD be unequal ; the solid SE is also ...
Página 234
... equal to the solid FY , because they are upon equal bases MK , PS , and of the same altitude , and have their insisting straight lines at right angles to the bases : and the so- lid EQ is equal to the solid AE ; and 234 THE ELEMENTS.
... equal to the solid FY , because they are upon equal bases MK , PS , and of the same altitude , and have their insisting straight lines at right angles to the bases : and the so- lid EQ is equal to the solid AE ; and 234 THE ELEMENTS.
Página 235
... altitude : therefore the solid AB is equal to the b 13.11 . solid GK , because they are upon e- qual bases AE , FH , and are of the same altitude : and because the solid parallelepi- ped CK is cut by B D K Q P L F the plane DG , A which ...
... altitude : therefore the solid AB is equal to the b 13.11 . solid GK , because they are upon e- qual bases AE , FH , and are of the same altitude : and because the solid parallelepi- ped CK is cut by B D K Q P L F the plane DG , A which ...
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Términos y frases comunes
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
Pasajes populares
Página 30 - Any two sides of a triangle are together greater than the third side.
Página 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.
Página 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...
Página 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.
Página 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 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.
Página 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.
Página 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.
Página 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.
Página 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.