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 89
... axis . For because AB ist equal to AC , and the portion of the axis intercepted between A and the intersection of BC with the axis is common , and the angle BAZ equal to CAZ ; BC ist bisected by the axis , and the angles at the ...
... axis . For because AB ist equal to AC , and the portion of the axis intercepted between A and the intersection of BC with the axis is common , and the angle BAZ equal to CAZ ; BC ist bisected by the axis , and the angles at the ...
Página 90
... axis ; the straight lines bisecting the several angles of the series ( being prolonged ) shall have met in the axis , in the part that is between the chord and the vertex . Let AB , AC , BD , CE , & c . be a series of equal straight ...
... axis ; the straight lines bisecting the several angles of the series ( being prolonged ) shall have met in the axis , in the part that is between the chord and the vertex . Let AB , AC , BD , CE , & c . be a series of equal straight ...
Página 91
... axis in some point between U and A. Let it cut it in S ; and join SC , SE , SG , & c . These shall be the straight lines bisecting the angles ACE , CEG , EGI , & c . of the series . * Constr . Cor . 7 . I. 6 . * I. 18 . INTERC . 1 . Cor ...
... axis in some point between U and A. Let it cut it in S ; and join SC , SE , SG , & c . These shall be the straight lines bisecting the angles ACE , CEG , EGI , & c . of the series . * Constr . Cor . 7 . I. 6 . * I. 18 . INTERC . 1 . Cor ...
Página 92
... axis , the straight lines bisecting the angles of the series shall in like manner have met in the axis , at its intersection with the chord . For the angle ILV will be equal to ILK , and the point S coincide with the point U. COR . 2 ...
... axis , the straight lines bisecting the angles of the series shall in like manner have met in the axis , at its intersection with the chord . For the angle ILV will be equal to ILK , and the point S coincide with the point U. COR . 2 ...
Página 93
... axis CAZ , the straight lines bisecting the angles of the series shall in like manner have met in the axis , at a point between O which is the intersection of the axis with WX , and the vertex A. For if the angle MNX is equal to CAZ ...
... axis CAZ , the straight lines bisecting the angles of the series shall in like manner have met in the axis , at a point between O which is the intersection of the axis with WX , and the vertex A. For if the angle MNX is equal to CAZ ...
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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.