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 ...Robert Heward, 1833 - 150 σελίδες |
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Σελίδα 56
... sides AB , AC of the one , equal to the two sides DE , DF of the other re- spectively , viz . AB to DE , and AC to DF ; and the angle BAC equal to the angle EDF . The third side BC shall be equal to the third side EF , and the triangle ...
... sides AB , AC of the one , equal to the two sides DE , DF of the other re- spectively , viz . AB to DE , and AC to DF ; and the angle BAC equal to the angle EDF . The third side BC shall be equal to the third side EF , and the triangle ...
Σελίδα 57
... sides AF , AC are equal to the two AG , AB re- spectively ; and the angle at A is common to the two triangles FAC , GAB ; therefore the third side FC ist equal to the third side GB , and the triangle FAC to the triangle GAB ; and the ...
... sides AF , AC are equal to the two AG , AB re- spectively ; and the angle at A is common to the two triangles FAC , GAB ; therefore the third side FC ist equal to the third side GB , and the triangle FAC to the triangle GAB ; and the ...
Σελίδα 58
... sides are equal to one another . Which was to be demonstrated . COR . 1. If two equal sides of any isoskeles 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 ...
... sides are equal to one another . Which was to be demonstrated . COR . 1. If two equal sides of any isoskeles 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 ...
Σελίδα 60
... Third Case ; where one of the vertices , as D , is upon a side of the other triangle . In this case BC and BD are not equal to one another ; for BC is the greater . And by parity of reasoning , the like may , in A any of the Cases , be ...
... Third Case ; where one of the vertices , as D , is upon a side of the other triangle . In this case BC and BD are not equal to one another ; for BC is the greater . And by parity of reasoning , the like may , in A any of the Cases , be ...
Σελίδα 61
... sides BA , AC , equal to the two sides DE , DF respectively , DG * INTERC.12 . Cor . 3 . + Hyp . I. 7 . B CE F viz . AB to DE , and AC to DF ; and also the third side BC equal to the third side EF . The angle BAC shall be equal to the ...
... sides BA , AC , equal to the two sides DE , DF respectively , DG * INTERC.12 . Cor . 3 . + Hyp . I. 7 . B CE F viz . AB to DE , and AC to DF ; and also the third side BC equal to the third side EF . The angle BAC shall be equal to the ...
Άλλες εκδόσεις - Προβολή όλων
Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Σελίδα 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 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.
Σελίδα 72 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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.
Σελίδα 103 - ... twice as many right angles as the figure has sides.
Σελίδα 70 - Any two angles of a triangle are together less than two right angles.
Σελίδα 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.
Σελίδα 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.