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 - Trigonometry - 518 pages |
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Results 6-10 of 89
Page 21
... likewise their sides terminated in the other extremity ; but this is impossible a ; therefore , if the base BC coincides with the a 7. 1 . base EF , the sides BA , AC cannot but coincide with the sides ED , DF ; wherefore , likewise ...
... likewise their sides terminated in the other extremity ; but this is impossible a ; therefore , if the base BC coincides with the a 7. 1 . base EF , the sides BA , AC cannot but coincide with the sides ED , DF ; wherefore , likewise ...
Page 25
... likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common angle ABC , the remaining angle ABE is equal to the remaining angle b 3. Ax , ABD , the less to the ...
... likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common angle ABC , the remaining angle ABE is equal to the remaining angle b 3. Ax , ABD , the less to the ...
Page 27
... likewise greater than the angle ACB ; wherefore much more is the angle ABC greater than ACB . Therefore , the greater side , & c . Q. E. D. PROP . XIX . THEOR . THE greater angle of every triangle is subtended by the greater side , or ...
... likewise greater than the angle ACB ; wherefore much more is the angle ABC greater than ACB . Therefore , the greater side , & c . Q. E. D. PROP . XIX . THEOR . THE greater angle of every triangle is subtended by the greater side , or ...
Page 28
... likewise equal to ACD ; but the angle BCD is great- D A er than the angle ACD ; therefore the angle BCD is greater than the B C c angle ADC ; and because the angle BCD of the triangle DCB c 19. 1. is greater than its angle BDC , and ...
... likewise equal to ACD ; but the angle BCD is great- D A er than the angle ACD ; therefore the angle BCD is greater than the B C c angle ADC ; and because the angle BCD of the triangle DCB c 19. 1. is greater than its angle BDC , and ...
Page 31
... equal to the two sides DE , DF , each to each , viz . AB equal to DE , and AC to DF ; but the base CB is greater than the base EF ; the angle BAC is likewise greater than the angle EDF . Book I. 24 1 . Α D For , if OF EUCLID . 31.
... equal to the two sides DE , DF , each to each , viz . AB equal to DE , and AC to DF ; but the base CB is greater than the base EF ; the angle BAC is likewise greater than the angle EDF . Book I. 24 1 . Α D For , if OF EUCLID . 31.
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Common terms and phrases
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
Popular passages
Page 30 - Any two sides of a triangle are together greater than the third side.
Page 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.
Page 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...
Page 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.
Page 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Page 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.
Page 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.
Page 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.
Page 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.
Page 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.