The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 17
... angle BAC equal to the angle EDF , the base BC fhall be equal to the bafe EF and the triangle ABC to the triangle DEF ; and the other angles , to which the equal fides are oppofite , fhall be equal each to each , viz . the angle ABCB to ...
... angle BAC equal to the angle EDF , the base BC fhall be equal to the bafe EF and the triangle ABC to the triangle DEF ; and the other angles , to which the equal fides are oppofite , fhall be equal each to each , viz . the angle ABCB to ...
Σελίδα 20
... angle ACB ; produce AC , AD to E , F ; therefore , becaufe AC is equal to AD in the triangle ACD , the angles ECD ... BAC is e- qual to the angle EDF . For , if the tri- DG angle ABC be ap- B plied to DEF , fo CE F that the point B be on ...
... angle ACB ; produce AC , AD to E , F ; therefore , becaufe AC is equal to AD in the triangle ACD , the angles ECD ... BAC is e- qual to the angle EDF . For , if the tri- DG angle ABC be ap- B plied to DEF , fo CE F that the point B be on ...
Σελίδα 21
... angle BAC coincides with the angle EDF , and is equal to it . There . b . s . Ax • fore if two triangles , & c . Q. E. D. T PROP . IX . PROB . O bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC ...
... angle BAC coincides with the angle EDF , and is equal to it . There . b . s . Ax • fore if two triangles , & c . Q. E. D. T PROP . IX . PROB . O bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC ...
Σελίδα 26
... BAC . Bifecta AC in E , join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE ... angle ACB ; therefore the angles ACD 26 THE ELEMENTS.
... BAC . Bifecta AC in E , join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE ... angle ACB ; therefore the angles ACD 26 THE ELEMENTS.
Σελίδα 27
... BAC , ACB , as also CAB , ABC are less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII . THEOR . HE greater fide of every triangle is oppofite to the T greater angle ... angle ABC is also greater than the angle ...
... BAC , ACB , as also CAB , ABC are less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII . THEOR . HE greater fide of every triangle is oppofite to the T greater angle ... angle ABC is also greater than the angle ...
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The First Six Books: Together with the Eleventh and Twelfth Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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Δημοφιλή αποσπάσματα
Σελίδα 474 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Σελίδα 170 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Σελίδα 105 - DEF are likewise equal (13. i.) to two right angles ; therefore the angles AKB, AMB are equal to the angles DEG, DEF, of which AKB is equal to DEG ; wherefore the remaining angle AMB is equal to the remaining angle DEF.
Σελίδα 167 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.
Σελίδα 10 - 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 62 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 112 - To describe an equilateral and equiangular pentagon about a given circle. • Let ABCDE be the given circle; it is required to describe an equilateral and equiangular pentagon about the circle ABCDE. Let the angles of a pentagon, inscribed in the circle...
Σελίδα 200 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.