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 93
Page 49
... reason , AB and AH are in the same straight line ; and because the angle DBC is e- qual to the angle FBA , each of them being a right angle , add to each the angle ABC , and the whole angle DBA is equal to the whole FBC ; and ...
... reason , AB and AH are in the same straight line ; and because the angle DBC is e- qual to the angle FBA , each of them being a right angle , add to each the angle ABC , and the whole angle DBA is equal to the whole FBC ; and ...
Page 54
... reason HF also is a square , and it is upon the side HG , which is equal to AC : therefore HF , CK are the squares of g 43. 1. AC , CB ; and because the complement AG is equal to the complement GE , and that AG is the rectangle ...
... reason HF also is a square , and it is upon the side HG , which is equal to AC : therefore HF , CK are the squares of g 43. 1. AC , CB ; and because the complement AG is equal to the complement GE , and that AG is the rectangle ...
Page 58
... reason , PR is equal to RO ; and because CB is equal to BD , and GK to KN , the rectangle CK is equal to BN , and GR to RN : but CK is equal to RN , because they are the complements of the parallelogram CO ; therefore also BN is equal ...
... reason , PR is equal to RO ; and because CB is equal to BD , and GK to KN , the rectangle CK is equal to BN , and GR to RN : but CK is equal to RN , because they are the complements of the parallelogram CO ; therefore also BN is equal ...
Page 59
... reason each of the angles CEB , EBC is half a right angle ; and therefore the whole AEB is a right angle and because the an- gle GEF is half a right angle , and EGF a right angle , for it is equal to the interior and oppo- site angle ...
... reason each of the angles CEB , EBC is half a right angle ; and therefore the whole AEB is a right angle and because the an- gle GEF is half a right angle , and EGF a right angle , for it is equal to the interior and oppo- site angle ...
Page 60
... the angle ACE is a right angle ; therefore each of the f32 . 1. angles CEA , EAC is half a right angle f : for the same reason , e 5. 1 . each of the angles CEB , EBC is half a 60 THE ELEMENTS Book II. the square of GF; but the ...
... the angle ACE is a right angle ; therefore each of the f32 . 1. angles CEA , EAC is half a right angle f : for the same reason , e 5. 1 . each of the angles CEB , EBC is half a 60 THE ELEMENTS Book II. the square of GF; but the ...
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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.