Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith |
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Page 13
... ABC , DEF , let AB = DE , and AC = DF , and △ BAC = △ EDF . Then must BC = EF and △ ABC = △ DEF , and the other △ s , to which the equal sides are opposite , must be equal , that ABC = L DEF and ACB = △ DFE . is , For , if △ ABC ...
... ABC , DEF , let AB = DE , and AC = DF , and △ BAC = △ EDF . Then must BC = EF and △ ABC = △ DEF , and the other △ s , to which the equal sides are opposite , must be equal , that ABC = L DEF and ACB = △ DFE . is , For , if △ ABC ...
Page 16
... ABC , let AC = AB . ( Fig . 1. ) Then must △ ABC = L ACB . Imagine the △ ABC to be taken up , turned round , and set down again in a reversed position as in Fig . 2 , and designate the angular points A ' , B ' , C ' . Then in As ABC ...
... ABC , let AC = AB . ( Fig . 1. ) Then must △ ABC = L ACB . Imagine the △ ABC to be taken up , turned round , and set down again in a reversed position as in Fig . 2 , and designate the angular points A ' , B ' , C ' . Then in As ABC ...
Page 17
... let ABC B E In As ABC , DEF , DEF , and △ ACB = 2 DFE , and BC = EF . Then must AB = DE , and AC = DF , and △ BAC = △ EDF . For if A DEF be applied to △ ABC , so that E coincides with B , and EF falls on BC ; then . EF - BC , .. F ...
... let ABC B E In As ABC , DEF , DEF , and △ ACB = 2 DFE , and BC = EF . Then must AB = DE , and AC = DF , and △ BAC = △ EDF . For if A DEF be applied to △ ABC , so that E coincides with B , and EF falls on BC ; then . EF - BC , .. F ...
Page 18
... Let the three sides of the As ABC , DEF be equal , each to each , that is , AB = DE , AC = DF , and BC = EF . Then must the triangles be equal in all respects . Imagine the DEF to be turned over and applied to the △ ABC , in such a way ...
... Let the three sides of the As ABC , DEF be equal , each to each , that is , AB = DE , AC = DF , and BC = EF . Then must the triangles be equal in all respects . Imagine the DEF to be turned over and applied to the △ ABC , in such a way ...
Page 25
... Let AB make with CD upon one side of it the 4s ABC , ABD . Then must these be either two rt . 28 , or together equal to two rt . 4 s . First , if △ ABC = △ ABD as in Fig . 1 , each of them is a rt . 4 . = Secondly , if ABC be not ...
... Let AB make with CD upon one side of it the 4s ABC , ABD . Then must these be either two rt . 28 , or together equal to two rt . 4 s . First , if △ ABC = △ ABD as in Fig . 1 , each of them is a rt . 4 . = Secondly , if ABC be not ...
Common terms and phrases
AB=DE ABCD AC=DF angles equal angular points base BC BC=EF centre chord circumference coincide described diagonals diameter divided equal angles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given angle given circle given point given st given straight line greater than nD hypotenuse inscribed intersect isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallelogram pentagon perpendicular produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rect rectangle contained reflex angle rhombus right angles segment shew shewn straight line joining subtended sum of sqq Take any pt tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Popular passages
Page 23 - 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 length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to AB from the point c. Take any point D upon the other side of AB, and from the centre c, at the distance CD, describe (Post.
Page 82 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 161 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Page 91 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Page 5 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 35 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.
Page 90 - ... the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse...
Page 265 - EQUAL parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles...