Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement ... to which are Added, Elements of Plane and Sphericale Trigonometry ... From the Last London Ed., Enl |
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Page 20
... interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the ex- terior angle ACD is greater than either of the interior opposite angles СВА , ВАС . Bisect ( 10. 1. ) AC in E , join BE and produce ...
... interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the ex- terior angle ACD is greater than either of the interior opposite angles СВА , ВАС . Bisect ( 10. 1. ) AC in E , join BE and produce ...
Page 21
... interior and opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are to- gether equal ( 13. 1. ) to two right an- A A B с D la gles : therefore ...
... interior and opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are to- gether equal ( 13. 1. ) to two right an- A A B с D la gles : therefore ...
Page 23
... interior and opposite angle , the exte- rior angle BDC of the triangle CDE is greater than CED : for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is ...
... interior and opposite angle , the exte- rior angle BDC of the triangle CDE is greater than CED : for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is ...
Page 27
... interior and opposite angle BCA , which is impossible ( 16. 1. ) ; wherefore BC is not unequal to EF , that is , it is equal to it ; and AB is equal to DE ; therefore the two , AB , BC are equal to the two DE , EF , each to each ; and ...
... interior and opposite angle BCA , which is impossible ( 16. 1. ) ; wherefore BC is not unequal to EF , that is , it is equal to it ; and AB is equal to DE ; therefore the two , AB , BC are equal to the two DE , EF , each to each ; and ...
Page 28
... interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles . Let the straight line EF fall upon the parallel straight lines AB , CD ; the alternate angles AGH ...
... interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles . Let the straight line EF fall upon the parallel straight lines AB , CD ; the alternate angles AGH ...
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Common terms and phrases
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference coincide cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
Popular passages
Page 3 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 112 - 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 64 - 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 38 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 5 - Let it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Page 280 - 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 sides.
Page 267 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Page 133 - ... cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Page 7 - If two triangles have two sides of the one equal to two sides of the...
Page 26 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.