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 σελίδες |
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Σελίδα xii
... extremity can have neither . And if the so - called extremity had length , it would not be the extremity , but part of the line . Thus the extremity of a line in the black surface above , is a point ; which manifestly has no dimensions ...
... extremity can have neither . And if the so - called extremity had length , it would not be the extremity , but part of the line . Thus the extremity of a line in the black surface above , is a point ; which manifestly has no dimensions ...
Σελίδα 26
... extremities of a straight line , ( inasmuch as the whole of the straight line remains without change of place ) is said to be turned round such straight line . When from any point to any other point , a straight line is described or ...
... extremities of a straight line , ( inasmuch as the whole of the straight line remains without change of place ) is said to be turned round such straight line . When from any point to any other point , a straight line is described or ...
Σελίδα 27
... extremities may be made to coincide . For if when one extremity of each are made to coincide , the other extremity of the one cannot be also made to coincide with the other extremity of the other ; then the extremity of one of them may ...
... extremities may be made to coincide . For if when one extremity of each are made to coincide , the other extremity of the one cannot be also made to coincide with the other extremity of the other ; then the extremity of one of them may ...
Σελίδα 28
... extremities of the proposed radius . COR . 7. If two spheres touch one another externally , the straight line which joins their centres shall pass through the point of contact . For it is one of the points through which the straight ...
... extremities of the proposed radius . COR . 7. If two spheres touch one another externally , the straight line which joins their centres shall pass through the point of contact . For it is one of the points through which the straight ...
Σελίδα 33
... extremities C and + INTERC.10 . D ) will cut BC and BD . Let it cut them in thet points E and F ; Cor . 9. wherefore BE , BF are ‡ equal . About E as a centre , with the radius EB , describe a sphere ; and about A as a centre , with the ...
... extremities C and + INTERC.10 . D ) will cut BC and BD . Let it cut them in thet points E and F ; Cor . 9. wherefore BE , BF are ‡ equal . About E as a centre , with the radius EB , describe a sphere ; and about A as a centre , with the ...
Άλλες εκδόσεις - Προβολή όλων
Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Σελίδα 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 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.
Σελίδα 72 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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.
Σελίδα 103 - ... twice as many right angles as the figure has sides.
Σελίδα 70 - Any two angles of a triangle are together less than two right angles.
Σελίδα 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.
Σελίδα 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.