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 iii
... half . TO WHICH IS ADDED AN APPENDIX Containing Notices of Methods at different times proposed for getting over the difficulty in the Twelfth Axiom of Euclid . Col By Thompson . By a Member of the University of Cambridge . * Perronet ...
... half . TO WHICH IS ADDED AN APPENDIX Containing Notices of Methods at different times proposed for getting over the difficulty in the Twelfth Axiom of Euclid . Col By Thompson . By a Member of the University of Cambridge . * Perronet ...
Página ix
... half , and in substance to the following . If a tessera [ or quadrilateral recti- linear plane figure of which two of the opposite sides are equal to one another and make equal interior angles with a side between them which shall be ...
... half , and in substance to the following . If a tessera [ or quadrilateral recti- linear plane figure of which two of the opposite sides are equal to one another and make equal interior angles with a side between them which shall be ...
Página 9
... half of a greater magnitude is greater than the half of a less . And so of any other equipartites . For , if it be not greater , it must either be equal or less . It cannot be equal , for then ( by Cor . 10 ) its double would be equal ...
... half of a greater magnitude is greater than the half of a less . And so of any other equipartites . For , if it be not greater , it must either be equal or less . It cannot be equal , for then ( by Cor . 10 ) its double would be equal ...
Página 11
... half , and from the remainder not less than its half , and so on ; there shall at length remain a magni- tude less than the least of the proposed magnitudes . A C D I E H F For if AB and C be the two proposed magnitudes , of which AB is ...
... half , and from the remainder not less than its half , and so on ; there shall at length remain a magni- tude less than the least of the proposed magnitudes . A C D I E H F For if AB and C be the two proposed magnitudes , of which AB is ...
Página 12
... half HI , and so on till the half be taken successively as many times as C was doubled successively to make DG ; the last remainder AI will be less than C. For as many times as C is con- tained in DG , so many times is AI contained in ...
... half HI , and so on till the half be taken successively as many times as C was doubled successively to make DG ; the last remainder AI will be less than C. For as many times as C is con- tained in DG , so many times is AI contained in ...
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.