Euclidian Geometry |
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Page 2
... its extremity A , towards the side on which BH is , so as to cut BH ; and thus two straight lines would enclose a space , which is impossible . Hence it follows that If two straight lines pass through 2 INTRODUCTION .
... its extremity A , towards the side on which BH is , so as to cut BH ; and thus two straight lines would enclose a space , which is impossible . Hence it follows that If two straight lines pass through 2 INTRODUCTION .
Page 3
... impossible . It is evident that Magnitudes which may be made to coincide , i.e. exactly fill the same space , are equal to one another . If two angles can be so placed that their vertices coincide and the arms of one fall along the arms ...
... impossible . It is evident that Magnitudes which may be made to coincide , i.e. exactly fill the same space , are equal to one another . If two angles can be so placed that their vertices coincide and the arms of one fall along the arms ...
Page 4
... impossible ; SO .. BC is = EF . Also the AABC will coincide with and is .. = LABC will coincide with and is .. LACB is = LDFE . △ DEF , DEF ; Hence the As ABC , DEF are equal in all respects . DEFINITION . An isosceles triangle is one ...
... impossible ; SO .. BC is = EF . Also the AABC will coincide with and is .. = LABC will coincide with and is .. LACB is = LDFE . △ DEF , DEF ; Hence the As ABC , DEF are equal in all respects . DEFINITION . An isosceles triangle is one ...
Page 17
... impossible . .. from a given point in a given straight line there cannot be drawn more than one straight line to it . COR . All right angles are equal to one another . X B C H K Let ABC , GHK be two right angles , and let the ABC be ...
... impossible . .. from a given point in a given straight line there cannot be drawn more than one straight line to it . COR . All right angles are equal to one another . X B C H K Let ABC , GHK be two right angles , and let the ABC be ...
Page 19
... impossible . ( hyp . ) ... no other straight line than BD is in the same straight line with BC ; .. BD is in the same straight line with BC . PROPOSITION XI . It is always possible to draw a 2-2 RIGHT ANGLES . 19 PROPOSITION X. ...
... impossible . ( hyp . ) ... no other straight line than BD is in the same straight line with BC ; .. BD is in the same straight line with BC . PROPOSITION XI . It is always possible to draw a 2-2 RIGHT ANGLES . 19 PROPOSITION X. ...
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Common terms and phrases
Algebra Arithmetic base BEGINNERS Cambridge centre chord Christ's College circumference cloth Conic Sections Crown 8vo Describe a circle diagonals diameter divided ELEMENTARY TREATISE English equiangular equilateral Euclid Examples Extra fcap GEOMETRY given angle given circle given point given straight line Grammar greater H Let Hence inscribed intersecting isosceles triangle John's College Latin Let ABC line bisecting locus magnitudes Mathematical meet Owens College parallel parallelogram perimeter perpendicular plane PROBLEM produced Professor proportional PROPOSITION radius ratio rect rectangle rectangle contained rectilineal figure regular polygon render respectively revised rhombus right angles Schools Second Edition segment Similarly squares on AC straight line joining student tangent THEOREM TRIGONOMETRY twice rectangle twice the squares Uppingham School vertex
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Page 157 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Page 15 - ... and the principles on which the observations made with these instruments are treated for deduction of the distances and weights of the bo.iits of the Solar System, and of a few stars, omitting all minutiit of Elementary Class- Books — continued. formulcE, and all troublesome details of calculation.