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 sider |
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Side 18
... common to the two triangles BFC , CGB ; wherefore the triangles are equal b , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to ...
... common to the two triangles BFC , CGB ; wherefore the triangles are equal b , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to ...
Side 19
... common to both , the two sides DB , BC are equal to to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB ...
... common to both , the two sides DB , BC are equal to to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB ...
Side 21
... common to the two triangles DAF , EAF ; the two sides DA , AF are equal to the two sides EA , AF , each to each ; and the base DF is D E equal to the base EF ; therefore the F angle DAF is equal to the angle B C c 8. 1 EAF ; wherefore ...
... common to the two triangles DAF , EAF ; the two sides DA , AF are equal to the two sides EA , AF , each to each ; and the base DF is D E equal to the base EF ; therefore the F angle DAF is equal to the angle B C c 8. 1 EAF ; wherefore ...
Side 22
... common to the two triangles ACD , BCD ; the two sides AC , CD are equal to BC , CD , each to each ; and the angle ACD is equal to the angle BCD ; there- fore the base AD is equal to the base c DB , and the straight line AB is divided ...
... common to the two triangles ACD , BCD ; the two sides AC , CD are equal to BC , CD , each to each ; and the angle ACD is equal to the angle BCD ; there- fore the base AD is equal to the base c DB , and the straight line AB is divided ...
Side 23
... common segment . A Ex PROP . XII . PROB . D B C TO draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any ...
... common segment . A Ex PROP . XII . PROB . D B C TO draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any ...
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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
Populære avsnitt
Side 30 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 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...
Side 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.
Side 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 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.
Side 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.
Side 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.
Side 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.
Side 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.