The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 121
... excess of the third above the fourth , is to the fourth . 17th prop . book 5 . XVII . Convertendo , by converfion ; when there are four proportion- als , and it is inferred , that the firft is to its excefs above the fecond Book V ...
... excess of the third above the fourth , is to the fourth . 17th prop . book 5 . XVII . Convertendo , by converfion ; when there are four proportion- als , and it is inferred , that the firft is to its excefs above the fecond Book V ...
Σελίδα 144
... excess above the fourth . a 17. 5 . b B. 5 . c 18. 5 . Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF. Because AB is to BE , as CD to DF , by divi- fion , AE is to EB , as CF to FD ; and by in- E verfion , BE is to EA ...
... excess above the fourth . a 17. 5 . b B. 5 . c 18. 5 . Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF. Because AB is to BE , as CD to DF , by divi- fion , AE is to EB , as CF to FD ; and by in- E verfion , BE is to EA ...
Σελίδα 149
... if the COR . 1. If the fame hypothefis be made as in the propofi- tion , the excess of the first and fifth fhall be to the fecond , as K 3 the a 22. 56 b 18. 5 " Book V. the excefs of the third and fixth to OF EUCLID . 149.
... if the COR . 1. If the fame hypothefis be made as in the propofi- tion , the excess of the first and fifth fhall be to the fecond , as K 3 the a 22. 56 b 18. 5 " Book V. the excefs of the third and fixth to OF EUCLID . 149.
Σελίδα 186
... excess of EF above C , and fimilar and fimilarly fituated to D ; but D is d . 21. 6. fimilar to EF , therefored alfo KM is fimilar to EF : Let KL be € 25. 6 . be the homologous fide to EG , and LM to 186 THE ELEMENTS.
... excess of EF above C , and fimilar and fimilarly fituated to D ; but D is d . 21. 6. fimilar to EF , therefored alfo KM is fimilar to EF : Let KL be € 25. 6 . be the homologous fide to EG , and LM to 186 THE ELEMENTS.
Σελίδα 255
... excess of the circle EFGH above S : Therefore the reft of the circle , viz . the polygon EKFLGMHN , is greater than the space S. Defcribe likewise in the circle ABCD the polygon AXBOCPDR fimilar to the polygon EKFLGMHN : As , therefore ...
... excess of the circle EFGH above S : Therefore the reft of the circle , viz . the polygon EKFLGMHN , is greater than the space S. Defcribe likewise in the circle ABCD the polygon AXBOCPDR fimilar to the polygon EKFLGMHN : As , therefore ...
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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
added alfo alſo altitude angle ABC angle BAC bafe baſe becauſe bifected Book Book XI centre circle circle ABCD circumference common cone cylinder defcribed definition demonftrated diameter divided double draw drawn equal equal angles equiangular equimultiples excefs fame fame multiple fecond fegment fhall fides fimilar firft folid folid angle fore four fourth fquare fquare of AC ftraight line given angle given in fpecies given in pofition given magnitude given ratio greater Greek half join lefs magnitude meet oppofite parallel parallelogram perpendicular plane prifms produced PROP propofition proportionals pyramid rectangle rectangle contained remaining right angles Take taken thefe THEOR theſe third triangle ABC wherefore whole
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.