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 páginas |
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Página 18
... fall on G and H. And after this let the sphere be turned round its centre again , till the points on its surface G and H coincide with E and F as before ; and let the sphere whose centre is B be likewise turned about its centre till the ...
... fall on G and H. And after this let the sphere be turned round its centre again , till the points on its surface G and H coincide with E and F as before ; and let the sphere whose centre is B be likewise turned about its centre till the ...
Página 55
... fall in some direction that will be deter- mined by the operations described in the preceding Problem , and will not , except by accident , coincide with the given straight line AB , from which a part equal to C is desired to be cut off ...
... fall in some direction that will be deter- mined by the operations described in the preceding Problem , and will not , except by accident , coincide with the given straight line AB , from which a part equal to C is desired to be cut off ...
Página 63
... falls on the side of it which is towards H , as EI . But because the angle IEF is equal to ABC , and IEH to ABG , and ABC and ABG are equal to one another , IEF and IEH must be ... fall on the side of ED which is BOOK I. - PROP . XI . 63.
... falls on the side of it which is towards H , as EI . But because the angle IEF is equal to ABC , and IEH to ABG , and ABC and ABG are equal to one another , IEF and IEH must be ... fall on the side of ED which is BOOK I. - PROP . XI . 63.
Página 64
... fall on the side of ED which is towards F ; and because it does not fall on either side of ED , it falls upon it , and the angle ABC coincides with the angle DEF , and is equal to it . And by parity of reasoning , the like may be proved ...
... fall on the side of ED which is towards F ; and because it does not fall on either side of ED , it falls upon it , and the angle ABC coincides with the angle DEF , and is equal to it . And by parity of reasoning , the like may be proved ...
Página 65
... fall upon the other , on the one side . COR . 2. All the angles made by any number of straight lines proceeding from ... fall on the side of BC which is towards A ; and in the same way may be shown , that it cannot fall on the other side ...
... fall upon the other , on the one side . COR . 2. All the angles made by any number of straight lines proceeding from ... fall on the side of BC which is towards A ; and in the same way may be shown , that it cannot fall on the other side ...
Otras ediciones - Ver todas
Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Sin vista previa disponible - 2015 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Página 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 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.
Página 72 - Any two sides of a triangle are together greater than the third side.
Página 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.
Página 103 - ... twice as many right angles as the figure has sides.
Página 70 - Any two angles of a triangle are together less than two right angles.
Página 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.
Página 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.