The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 320
... given the demonstration of the 10th proposition as we now have it , instead of that which Eudoxus or Euclid had given , has been deceived in applying what is manifest , when understood of magnitudes , unto ratios , viz . that a magnitude ...
... given the demonstration of the 10th proposition as we now have it , instead of that which Eudoxus or Euclid had given , has been deceived in applying what is manifest , when understood of magnitudes , unto ratios , viz . that a magnitude ...
Σελίδα 338
... given straight line that shall be equal to a given rectangle , exceeding by a square . Let AB be the given straight ... magnitude of it being likewife given , to find its fides . And the 4th problem is the fame with this , To find ...
... given straight line that shall be equal to a given rectangle , exceeding by a square . Let AB be the given straight ... magnitude of it being likewife given , to find its fides . And the 4th problem is the fame with this , To find ...
Σελίδα 339
Together with the Eleventh and Twelfth Euclid. F 1 Nin the given straight line AB produced , so as to make the Book ... magnitude of it , to find the fides . PROP . XXXI . B. VI . In the demonstration of this , the inversion of ...
Together with the Eleventh and Twelfth Euclid. F 1 Nin the given straight line AB produced , so as to make the Book ... magnitude of it , to find the fides . PROP . XXXI . B. VI . In the demonstration of this , the inversion of ...
Σελίδα 341
... magnitude , that are neither similar nor equal , as shall be demonstrated after the notes on the 10th definition ... given no definition of e- qual figures , and it is certain he did not give this : For what is called the ist def ...
... magnitude , that are neither similar nor equal , as shall be demonstrated after the notes on the 10th definition ... given no definition of e- qual figures , and it is certain he did not give this : For what is called the ist def ...
Σελίδα 344
... magnitude D which is less than A , B , C together , but greater than the excess of A above B and C : Then B , C , D together are greater than A ; and because A is greater than ei- ther B or C , much more will A and D , together with ...
... magnitude D which is less than A , B , C together , but greater than the excess of A above B and C : Then B , C , D together are greater than A ; and because A is greater than ei- ther B or C , much more will A and D , together with ...
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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
alſo altitude angle ABC angle BAC baſe BC is equal BC is given becauſe the angle becauſe the ratio biſected Book XI cafe cauſe centre circle ABCD circumference cone conſtruction cylinder demonſtration deſcribed diameter drawn EFGH equal angles equiangular equimultiples Euclid exceſs fame manner fame multiple fame ratio fame reaſon fides fimilar firſt folid angle fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join leſs line BC oppoſite parallel parallelepipeds parallelogram perpendicular plane angles priſm proportionals propoſition pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſide ſolid ſome ſpace ſphere ſquare of BC THEOR theſe thoſe triangle ABC vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 482 - 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.