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 62
... bisected in G. Which was to be done . And by parity of reasoning , in like manner may every other given straight line be bisected . PROPOSITION X. PROBLEM . - To draw a straight line at right angles to an assigned straight line , from ...
... bisected in G. Which was to be done . And by parity of reasoning , in like manner may every other given straight line be bisected . PROPOSITION X. PROBLEM . - To draw a straight line at right angles to an assigned straight line , from ...
Seite 68
... bisected by the straight line AF . Second Case ; if the angle BAC is equal to the sum of two right angles , BAC will be ‡ in one and the same straight line , and DE be bisected by the point A , and AF be perpendicular to BAC and bisect ...
... bisected by the straight line AF . Second Case ; if the angle BAC is equal to the sum of two right angles , BAC will be ‡ in one and the same straight line , and DE be bisected by the point A , and AF be perpendicular to BAC and bisect ...
Seite 69
... Bisect + CA , in E ; join BE , and prolong it to F ; and make ‡ 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 to EC and EF respectively . Also the angle AEB is ...
... Bisect + CA , in E ; join BE , and prolong it to F ; and make ‡ 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 to EC and EF respectively . Also the angle AEB is ...
Seite 70
... bisected , may be shown that the angle BCG is greater than CBA . But the angle BCG ist equal to ACD , for they are vertical angles ; therefore INTERC . 1. the angle ACD is also greater than CBA . And in the same way may be shown that ...
... bisected , may be shown that the angle BCG is greater than CBA . But the angle BCG ist equal to ACD , for they are vertical angles ; therefore INTERC . 1. the angle ACD is also greater than CBA . And in the same way may be shown that ...
Seite 76
... Bisect + CF , in G ; and join DG . Because in the triangles CDG , FDG , DC ist equal to DF , and CG to * FG , and DG is ... bisected by the straight line DB , DG and DB are † in + I. 9. Cor . one straight line ; wherefore EB shall pass ...
... Bisect + CF , in G ; and join DG . Because in the triangles CDG , FDG , DC ist equal to DF , and CG to * FG , and DG is ... bisected by the straight line DB , DG and DB are † in + I. 9. Cor . one straight line ; wherefore EB shall pass ...
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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.