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 ... |
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Page viii
... continually before the senses ; but these are not self - evident , but proved by the con- tinual evidence of the senses . There may be things whose connexion with other things is so constantly impressed upon us by experience , that few ...
... continually before the senses ; but these are not self - evident , but proved by the con- tinual evidence of the senses . There may be things whose connexion with other things is so constantly impressed upon us by experience , that few ...
Page 87
... continually ; and the extremities of every two equal straight lines so successively added at one and the same time at the two ends of the series , be joined by a straight line or chord ; each of these chords shall make the angles at the ...
... continually ; and the extremities of every two equal straight lines so successively added at one and the same time at the two ends of the series , be joined by a straight line or chord ; each of these chords shall make the angles at the ...
Page 90
... continually increasing , this is not sufficient to prove that it will ever arrive at a certain specified greatness ; as , for instance , that it will ever be so great as a right angle , or as CAZ , or even as twice the angle ACB ...
... continually increasing , this is not sufficient to prove that it will ever arrive at a certain specified greatness ; as , for instance , that it will ever be so great as a right angle , or as CAZ , or even as twice the angle ACB ...
Page 94
... continually on both sides , for as many as shall at any time be desired . Because the angles MAB , NBA , MAC , OCA , & c . are equal to one another and each less than a right angle , and the straight lines AB , AC , BD , CE , & c . are ...
... continually on both sides , for as many as shall at any time be desired . Because the angles MAB , NBA , MAC , OCA , & c . are equal to one another and each less than a right angle , and the straight lines AB , AC , BD , CE , & c . are ...
Page 98
... continually prolonged , shall at length meet on that side of the other straight line on which are the angles which are together less than two right angles . Let the two straight lines AB and CD which are in the same plane , be met by ...
... continually prolonged , shall at length meet on that side of the other straight line on which are the angles which are together less than two right angles . Let the two straight lines AB and CD which are in the same plane , be met by ...
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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.