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 17
Side 77
... point A in one of them , a straight line be drawn perpendicular to the other ; the perpendicular shall fall on that side of C , on which is the acute angle ... angular point a perpen- dicular CD be drawn to the side ; the per- pendicular ...
... point A in one of them , a straight line be drawn perpendicular to the other ; the perpendicular shall fall on that side of C , on which is the acute angle ... angular point a perpen- dicular CD be drawn to the side ; the per- pendicular ...
Side 89
... angle BAC be bisected by a straight line AZ of unlimited length , such straight line is called the axis of the series ; the point A is called the vertex ; and the angle CAZ or BAZ , the angle with the axis . COR . 1. If the angular points ...
... angle BAC be bisected by a straight line AZ of unlimited length , such straight line is called the axis of the series ; the point A is called the vertex ; and the angle CAZ or BAZ , the angle with the axis . COR . 1. If the angular points ...
Side 92
... angle SCA is † equal to SAC . And the Hyp . * INTERC . 1. angle SAC is ‡ half the angle BAC , therefore SCA is * equal to half ... points G , & c . to S. + I . 14. Cor . But becauset only one straight line ... angular 92 EUCLID'S ELEMENTS .
... angle SCA is † equal to SAC . And the Hyp . * INTERC . 1. angle SAC is ‡ half the angle BAC , therefore SCA is * equal to half ... points G , & c . to S. + I . 14. Cor . But becauset only one straight line ... angular 92 EUCLID'S ELEMENTS .
Side 93
... angular points , make with it on the side remote from the vertex an angle MNX equal to or less than the angle with the axis CAZ , the straight lines bisecting the angles of the series shall in like manner have met in the axis , at a point ...
... angular points , make with it on the side remote from the vertex an angle MNX equal to or less than the angle with the axis CAZ , the straight lines bisecting the angles of the series shall in like manner have met in the axis , at a point ...
Side 95
... angle each way , greater * than a given angle ABC . And on the side towards Z , it will at all times make an in- terior angle each way , greater than a given angle BAZ . For when WX arrives at any of the angular points ( as D , E ) ...
... angle each way , greater * than a given angle ABC . And on the side towards Z , it will at all times make an in- terior angle each way , greater than a given angle BAZ . For when WX arrives at any of the angular points ( as D , E ) ...
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.