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 sider |
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Resultat 6-10 av 23
Side 69
... equal . PROPOSITION XV . THEOREM . - If two straight lines cut one another , the vertical angles shall be equal ... EF equal to EB . Join also FC ; and prolong AC to G. Because EA is * equal to EC , and EB to * EF , EA and EB are equal ...
... equal . PROPOSITION XV . THEOREM . - If two straight lines cut one another , the vertical angles shall be equal ... EF equal to EB . Join also FC ; and prolong AC to G. Because EA is * equal to EC , and EB to * EF , EA and EB are equal ...
Side 78
... EF . Of the two sides AB , AC , let AB be one that is not greater than the other ; and at the point A in the straight line * 1.22.Cor.2 . AB , make * the angle BAI equal to the angle EDF . Because AB is not greater than AC , the angle ...
... EF . Of the two sides AB , AC , let AB be one that is not greater than the other ; and at the point A in the straight line * 1.22.Cor.2 . AB , make * the angle BAI equal to the angle EDF . Because AB is not greater than AC , the angle ...
Side 79
... equal to them , of the other . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two DE , DF respectively , viz . AB to DE , and AC to DF ; but the third side BC is greater than the third side EF . The angle A ...
... equal to them , of the other . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two DE , DF respectively , viz . AB to DE , and AC to DF ; but the third side BC is greater than the third side EF . The angle A ...
Side 80
... equal to EF which lies between the angles DEF and DFE in the triangle DEF . G AA B The remaining angle BAC shall be equal to the remaining angle EDF ; and the triangle ABC to the triangle DEF ; and their other sides , which are opposite to ...
... equal to EF which lies between the angles DEF and DFE in the triangle DEF . G AA B The remaining angle BAC shall be equal to the remaining angle EDF ; and the triangle ABC to the triangle DEF ; and their other sides , which are opposite to ...
Side 81
... equal to EF , let BC be assumed to be the greater ; and make * BH equal to EF , and join AH . Because BH is equal to EF , and BA to † ED , BH and BA are equal to EF and ED respectively . Also the angle ABH ist equal to the angle DEF ...
... equal to EF , let BC be assumed to be the greater ; and make * BH equal to EF , and join AH . Because BH is equal to EF , and BA to † ED , BH and BA are equal to EF and ED respectively . Also the angle ABH ist equal to the angle DEF ...
Andre utgaver - Vis alle
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... Thomas Perronet Thompson Uten tilgangsbegrensning - 1833 |
Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Side 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 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.
Side 72 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 70 - Any two angles of a triangle are together less than two right angles.
Side 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.
Side 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.