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 1-5 av 53
Side 28
... joins their centres shall pass through the point of contact . For it is one of the points through which the straight line + INTERC.10 . described as by Prop . IX , passes . And there can bet no other straight line between the centres ...
... joins their centres shall pass through the point of contact . For it is one of the points through which the straight line + INTERC.10 . described as by Prop . IX , passes . And there can bet no other straight line between the centres ...
Side 33
... joining their centres ; + INTERC . 10. the spheres touch † one another externally in the point B. And if the straight line AC , together with the two substantial spheres whose centres are A and E , be turned about the points A and C ...
... joining their centres ; + INTERC . 10. the spheres touch † one another externally in the point B. And if the straight line AC , together with the two substantial spheres whose centres are A and E , be turned about the points A and C ...
Side 38
... join CF , + INTERC.12 and let CF bet prolonged to an unlimited length on the side Cor . 6. of L. Let then the spheres BFGH and AFIH be united as one INTERC . 9. body , and together with the straight line CL be turned round the Nom ...
... join CF , + INTERC.12 and let CF bet prolonged to an unlimited length on the side Cor . 6. of L. Let then the spheres BFGH and AFIH be united as one INTERC . 9. body , and together with the straight line CL be turned round the Nom ...
Side 39
... join AM , BM ; and afterwards let the united spheres be transposed , and turned round BA till M be in the same place ... joins their centres must * pass through M , and it does not ; wherefore they will cut one another in one self ...
... join AM , BM ; and afterwards let the united spheres be transposed , and turned round BA till M be in the same place ... joins their centres must * pass through M , and it does not ; wherefore they will cut one another in one self ...
Side 40
... join * INTERC.10 . AM , AQ , BM , BQ , and these straight lines will be ‡ all equal one to another , because they are radii of the same or equal spheres ; where- Cor . 4 . G D M N N H EI fore if about the centres M and Q , and. 40 ...
... join * INTERC.10 . AM , AQ , BM , BQ , and these straight lines will be ‡ all equal one to another , because they are radii of the same or equal spheres ; where- Cor . 4 . G D M N N H EI fore if about the centres M and Q , and. 40 ...
Andre utgaver - Vis alle
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.