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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Αποτελέσματα 1 - 5 από τα 13.
Σελίδα 34
... aret equal but do not coincide , and the point B INTERC.11 . is in the surface of both ; they will cut one another in a self - rejoining line passing through B , or else touch in B only . But whichever of these they do , ( inasmuch as ...
... aret equal but do not coincide , and the point B INTERC.11 . is in the surface of both ; they will cut one another in a self - rejoining line passing through B , or else touch in B only . But whichever of these they do , ( inasmuch as ...
Σελίδα 56
... aret equal . And because the straight line AC is equal to DF , the point C would coincide with the point F. But the point B coincides with the point E ; wherefore ( the point B coin- ciding with E , and C with F , ) the straight line BC ...
... aret equal . And because the straight line AC is equal to DF , the point C would coincide with the point F. But the point B coincides with the point E ; wherefore ( the point B coin- ciding with E , and C with F , ) the straight line BC ...
Σελίδα 72
... aret together greater than CB . In the same way by prolonging AC , may be shown that the sides AC and CB are together greater than BA ; and by prolonging CB , may be shown that CB and BA are together greater than AC . + INTERC . 1 . Cor ...
... aret together greater than CB . In the same way by prolonging AC , may be shown that the sides AC and CB are together greater than BA ; and by prolonging CB , may be shown that CB and BA are together greater than AC . + INTERC . 1 . Cor ...
Σελίδα 76
... aret together equal to four right angles ; DC and DF make an angle less than two right angles , either on one side or the other . Wherefore CF will * form a triangle with them , on that side on which is the angle CDF that is less than ...
... aret together equal to four right angles ; DC and DF make an angle less than two right angles , either on one side or the other . Wherefore CF will * form a triangle with them , on that side on which is the angle CDF that is less than ...
Σελίδα 88
... aret equal to one another , DBEG is also a tessera ; and in the same manner may be shown that FDGI , & c . are likewise tesseras . And because the angle ABE is greater than ABC , and Cor . 2 . the angle CEB has been shown 88 EUCLID'S ...
... aret equal to one another , DBEG is also a tessera ; and in the same manner may be shown that FDGI , & c . are likewise tesseras . And because the angle ABE is greater than ABC , and Cor . 2 . the angle CEB has been shown 88 EUCLID'S ...
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.