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 vi
... follows . A solid may be described , all the points in whose surface shall be equidistant from a given point within ; such a solid is called a sphere . A sphere may be turned in any manner whatsoever about its centre , without change of ...
... follows . A solid may be described , all the points in whose surface shall be equidistant from a given point within ; such a solid is called a sphere . A sphere may be turned in any manner whatsoever about its centre , without change of ...
Página vii
... follows , but to take advantage of the habits of rea- soning that may be thus acquired , before attempting what must be characterized as , in some parts , at least equal in complexity to anything in the succeeding Books . If this ...
... follows , but to take advantage of the habits of rea- soning that may be thus acquired , before attempting what must be characterized as , in some parts , at least equal in complexity to anything in the succeeding Books . If this ...
Página 2
... follow , as , for instance , that the sum of them shall be equal to some third magnitude ; one of these magnitudes may at any period of the operations in hand be avouched to be equal to the other by the hypothesis . For that they are ...
... follow , as , for instance , that the sum of them shall be equal to some third magnitude ; one of these magnitudes may at any period of the operations in hand be avouched to be equal to the other by the hypothesis . For that they are ...
Página 4
... follows : - : - The first conveys a statement of the universal proposition to be finally established . Which is called the enunciation . The second presents to the eye , or to the imagination , a particular instance , in respect of ...
... follows : - : - The first conveys a statement of the universal proposition to be finally established . Which is called the enunciation . The second presents to the eye , or to the imagination , a particular instance , in respect of ...
Página 57
... angle GCB , and the angle BCF to CBG . And since it has been demonstrated that the whole angle ACF is equal to the whole angle ABG , parts of which , the angles * I. 4 . BCF and CBG , are also equal ; it follows BOOK I. - PROP . V. 57.
... angle GCB , and the angle BCF to CBG . And since it has been demonstrated that the whole angle ACF is equal to the whole angle ABG , parts of which , the angles * I. 4 . BCF and CBG , are also equal ; it follows BOOK I. - PROP . V. 57.
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.