Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 σελίδες |
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Αποτελέσματα 1 - 5 από τα 82.
Σελίδα 10
... equal , when , applied to each other , they wholly coincide ; they are equivalent , if , with- out coinciding , they yet contain the same space . A PROPOSITION is a distinct portion of abstract science . 10 ELEMENTS OF GEOMETRY .
... equal , when , applied to each other , they wholly coincide ; they are equivalent , if , with- out coinciding , they yet contain the same space . A PROPOSITION is a distinct portion of abstract science . 10 ELEMENTS OF GEOMETRY .
Σελίδα 44
... equivalent . The triangles ABC and ADC which stand on the same base AC and have the same altitude , contain equal ... equivalent to ADFC . Whence the tri- angles ABC and ADC , which are the halves of these rhom- boids ( I. 26. cor ...
... equivalent . The triangles ABC and ADC which stand on the same base AC and have the same altitude , contain equal ... equivalent to ADFC . Whence the tri- angles ABC and ADC , which are the halves of these rhom- boids ( I. 26. cor ...
Σελίδα 45
... equivalent . The triangles ABC , DEF , standing on equal bases AC and DF and having the same altitude , contain ... equivalent to AE ( II . 1. cor . ) , and this again is , for the same reason , equivalent to HF ; consequently GC is ...
... equivalent . The triangles ABC , DEF , standing on equal bases AC and DF and having the same altitude , contain ... equivalent to AE ( II . 1. cor . ) , and this again is , for the same reason , equivalent to HF ; consequently GC is ...
Σελίδα 46
... Equivalent triangles on the same or equal bases , have the same altitude . If the triangles ABC and ADC , standing ... equivalent to AEC ; but ABC is by hypothesis equivalent to ADC , and therefore AEC is equivalent to ADC , which is ...
... Equivalent triangles on the same or equal bases , have the same altitude . If the triangles ABC and ADC , standing ... equivalent to AEC ; but ABC is by hypothesis equivalent to ADC , and therefore AEC is equivalent to ADC , which is ...
Σελίδα 47
... equivalent to the five - sided figure ABCDE . A F E D Because the triangles CFA and CBA have by construc- tion the same altitude and stand on the same base AC , they are ( II . 1. ) equivalent ; take each of them away from the space ...
... equivalent to the five - sided figure ABCDE . A F E D Because the triangles CFA and CBA have by construc- tion the same altitude and stand on the same base AC , they are ( II . 1. ) equivalent ; take each of them away from the space ...
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Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angle altitude angle ABC angle ADB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter side AC sides AB sine square of AC squares of AB straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 30 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Σελίδα 333 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Σελίδα 294 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Σελίδα 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 137 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Σελίδα 84 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Σελίδα 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Σελίδα 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Σελίδα 38 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.