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 Seiten |
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Seite 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 the triangle EDF ; and the other angles , to which the equal sides are opposite , shall be equal respectively , viz . the ...
... angle BAC equal to the angle EDF . The third side BC shall be equal to the third side EF , and the triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall be equal respectively , viz . the ...
Seite 57
... 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 lengths , as for ...
... 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 lengths , as for ...
Seite 58
... angle ACB equal to the angle ABC . Cor . 7 . See Note . + INTERC . 1 . And by parity of reasoning , the like may be ... BAC be a triangle having the angle ACB equal to the angle ABC ; the side BA is equal to the side CA. C For if BA be ...
... angle ACB equal to the angle ABC . Cor . 7 . See Note . + INTERC . 1 . And by parity of reasoning , the like may be ... BAC be a triangle having the angle ACB equal to the angle ABC ; the side BA is equal to the side CA. C For if BA be ...
Seite 61
... angle which is between the two sides of the one , shall be equal to the ... BAC , EDF be two triangles , having the two sides BA , AC , equal to the two ... angle BAC shall be equal to the angle EDF ; and the triangle BAC to the triangle ...
... angle which is between the two sides of the one , shall be equal to the ... BAC , EDF be two triangles , having the two sides BA , AC , equal to the two ... angle BAC shall be equal to the angle EDF ; and the triangle BAC to the triangle ...
Seite 68
... a given angle . [ That is , to divide it into two equal angles . ] R 1.3 . † 1. 1 . Constr . Constr . + I . 8 . II . 13 . Let BAC be the given angle . It is required to bisect it . D E First Case ; if BAC is less than the sum of two right ...
... a given angle . [ That is , to divide it into two equal angles . ] R 1.3 . † 1. 1 . Constr . Constr . + I . 8 . II . 13 . Let BAC be the given angle . It is required to bisect it . D E First Case ; if BAC is less than the sum of two right ...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Seite 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Seite 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.
Seite 72 - Any two sides of a triangle are together greater than the third side.
Seite 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.
Seite 103 - ... twice as many right angles as the figure has sides.
Seite 70 - Any two angles of a triangle are together less than two right angles.
Seite 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.
Seite 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.