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 22
Side 77
... angle but an acute angle . Neither can it fall on the side of C on which is the obtuse angle , as for instance upon the point B ; for since ACD ( which is the exterior angle of the triangle ACB ) is less than a right angle , still more ...
... angle but an acute angle . Neither can it fall on the side of C on which is the obtuse angle , as for instance upon the point B ; for since ACD ( which is the exterior angle of the triangle ACB ) is less than a right angle , still more ...
Side 78
... angle EDF . Because AB is not greater than AC , the angle ACB is not greater than ABC ; for if it was greater , AB the side opposite to it would be † greater than AC the side opposite to the other . Again , the exterior angle AHC is ...
... angle EDF . Because AB is not greater than AC , the angle ACB is not greater than ABC ; for if it was greater , AB the side opposite to it would be † greater than AC the side opposite to the other . Again , the exterior angle AHC is ...
Side 81
... angle AHB ( which was shown to be equal to DFE ) must be ‡ equal to ACH , the exterior angle equal to the interior and op- posite , which is * impossible . It cannot be , therefore , that BC is greater than EF ; and in the same manner ...
... angle AHB ( which was shown to be equal to DFE ) must be ‡ equal to ACH , the exterior angle equal to the interior and op- posite , which is * impossible . It cannot be , therefore , that BC is greater than EF ; and in the same manner ...
Side 82
... triangle , and its exterior angle GHC greater than the interior opposite angle HGI . Which is impossible , for it is equal to it . It cannot be , therefore , that AB and CD being prolonged , will meet on the side of B and D. And in the ...
... triangle , and its exterior angle GHC greater than the interior opposite angle HGI . Which is impossible , for it is equal to it . It cannot be , therefore , that AB and CD being prolonged , will meet on the side of B and D. And in the ...
Side 83
... interior angles on the same side , together equal to two right angles ; those two straight lines shall be parallel . E G B C H D F For First ; where the exterior angle EGA is equal to the interior and opposite angle A GHC . Because the ...
... interior angles on the same side , together equal to two right angles ; those two straight lines shall be parallel . E G B C H D F For First ; where the exterior angle EGA is equal to the interior and opposite angle A GHC . Because the ...
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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.