Geometry Without Axioms; Or the First Book of Euclid's Elements. With Alterations and Familiar Notes; and an Intercalary Book in which the Straight Line and Plane are Derived from Properties of the Sphere ...: To which is Added an Appendix ... |
From inside the book
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Page 50
... angle between them . B A D -C E Hence angles are compared together by their extension sideways only ; without ... ABC , or CBA ; that between BA and BD , is na ed the angle ABD , or DBA ; and that between BD and BC , is named the angle ...
... angle between them . B A D -C E Hence angles are compared together by their extension sideways only ; without ... ABC , or CBA ; that between BA and BD , is na ed the angle ABD , or DBA ; and that between BD and BC , is named the angle ...
Page 56
... angle BAC equal to the angle EDF . The third side BC shall be equal to the third side EF , and the triangle BAC to ... ABC to the angle DEF , and the angle ACB to the angle DFE . * For , if the triangle BAC was applied to the triangle ...
... angle BAC equal to the angle EDF . The third side BC shall be equal to the third side EF , and the triangle BAC to ... ABC to the angle DEF , and the angle ACB to the angle DFE . * For , if the triangle BAC was applied to the triangle ...
Page 57
... triangle , the angles opposite to two equal sides are equal to one another . Let BAC be an isoskeles triangle , of which the side AB is equal to AC . The angles ACB and ABC shall be equal to one another . Prolong * AB and AC to any ...
... triangle , the angles opposite to two equal sides are equal to one another . Let BAC be an isoskeles triangle , of which the side AB is equal to AC . The angles ACB and ABC shall be equal to one another . Prolong * AB and AC to any ...
Page 58
... triangle be pro- longed , the two angles exterior to the third side shall be equal . For the angle FBC was shown to be equal to GCB . A B COR . 2. Every equilateral triangle is also equiangular . For if ABC be an equilateral triangle ...
... triangle be pro- longed , the two angles exterior to the third side shall be equal . For the angle FBC was shown to be equal to GCB . A B COR . 2. Every equilateral triangle is also equiangular . For if ABC be an equilateral triangle ...
Page 59
... triangle whereof two angles are equal to one another . Wherefore , universally , if two angles & c . Which was to be demonstrated . COR . Every equiangular triangle is also equilateral . For if ABC be a triangle of which all the angles ...
... triangle whereof two angles are equal to one another . Wherefore , universally , if two angles & c . Which was to be demonstrated . COR . Every equiangular triangle is also equilateral . For if ABC be a triangle of which all the angles ...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson No preview available - 2015 |
Common terms and phrases
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angular points assigned point Axiom axis base BC bisected called CEGDHF central distances change of place circle coincide throughout Constr demonstrated double equal angles equal straight lines equal to AC equal to EF equilateral triangle Euclid exterior angle extremities four right angles Geometry given straight line greater half the angle hard body inclose a space instance INTERC Intercalary Book ist equal join line AC magnitude manner meet opposite angles parallelogram parity of reasoning pass perpendicular prolonged Prop PROPOSITION proved quadrilateral radii radius rectilinear figure remain unmoved remaining angle remains at rest respectively SCHOLIUM self-rejoining line shown side BC side opposite situation sphere whose centre straight line BC tessera THEOREM.-If third side triangle ABC turned unlimited length Wherefore
Popular passages
Page 51 - 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 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Page 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Page 120 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Page 72 - Any two sides of a triangle are together greater than the third side.
Page 55 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Page 103 - ... twice as many right angles as the figure has sides.
Page 70 - Any two angles of a triangle are together less than two right angles.
Page 138 - ... the exterior angle equal to the interior and opposite on the same side of the line ; and likewise the two interior angles on the same side of the line together equal to two right angles.
Page 106 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.