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 20
... sides of the one shall be equal to the angle contained by the two sides equal to them , of the other . Let ABC , DEF be two triangles , having the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to DE , and AC ...
... sides of the one shall be equal to the angle contained by the two sides equal to them , of the other . Let ABC , DEF be two triangles , having the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to DE , and AC ...
Seite 21
... sides BA , CA do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then , upon the same base EF , and upon the same side of it , there can be two triangles that have their sides which are terminated in ...
... sides BA , CA do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then , upon the same base EF , and upon the same side of it , there can be two triangles that have their sides which are terminated in ...
Seite 27
... side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC is also greater than the angle BCA . Because AC is greater than AB , make AD equal to AB ...
... side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC is also greater than the angle BCA . Because AC is greater than AB , make AD equal to AB ...
Seite 28
... side . Let ABC be a triangle ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA great- er than AB . Produce BA to the point D ...
... side . Let ABC be a triangle ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA great- er than AB . Produce BA to the point D ...
Seite 29
... sides BA , AC are greater than BE , EC : again , because the two sides CE , ED of the triangle CED are great- er than CD , add DB to each of these ; therefore the sides CE , EB are greater than CD , DB ; but it has been shown that BA ...
... sides BA , AC are greater than BE , EC : again , because the two sides CE , ED of the triangle CED are great- er than CD , add DB to each of these ; therefore the sides CE , EB are greater than CD , DB ; but it has been shown that BA ...
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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.