The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 51
... number of parts ; the rectangle contained by the two ftraight lines , is equal to the rectangles contain- ed by the undivided line , and the feveral parts of the divided line . D 2 Let Book II . Book II . a 11. I ' b 3. I. OF EUCLID . 51.
... number of parts ; the rectangle contained by the two ftraight lines , is equal to the rectangles contain- ed by the undivided line , and the feveral parts of the divided line . D 2 Let Book II . Book II . a 11. I ' b 3. I. OF EUCLID . 51.
Σελίδα 52
... rectangle contained by the straight lines A , BC is equal to the rectangle contained by A , BD , together with that contain- ed by A , DE , and that contained by A , EC . KLH A From the point B draw BF at right angles to BC , and makeG ...
... rectangle contained by the straight lines A , BC is equal to the rectangle contained by A , BD , together with that contain- ed by A , DE , and that contained by A , EC . KLH A From the point B draw BF at right angles to BC , and makeG ...
Σελίδα 53
... rectangle contained by AB , AC , together with the rectangle AB , BC , is equal to the fquare of AB . If therefore a straight line , & c . Q. E. D. PROP . III . THEOR . Fa ftraight line be divided into any two parts , the rectangle ...
... rectangle contained by AB , AC , together with the rectangle AB , BC , is equal to the fquare of AB . If therefore a straight line , & c . Q. E. D. PROP . III . THEOR . Fa ftraight line be divided into any two parts , the rectangle ...
Σελίδα 54
... rectangle contain . ed by AC , CB , for GC is equal to CB ; therefore GE is alfo equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB : And HF , CK are the fquares of AC , CB ; wherefore the four ...
... rectangle contain . ed by AC , CB , for GC is equal to CB ; therefore GE is alfo equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB : And HF , CK are the fquares of AC , CB ; wherefore the four ...
Σελίδα 55
... rectangle con- tained by the unequal parts , together with the fquare of the line between the points of fection , is ... contained by AD , DB , for DH is equal C DB d 36. I. L H M EGF 2 . to DB ; and DF together with CH is the ...
... rectangle con- tained by the unequal parts , together with the fquare of the line between the points of fection , is ... contained by AD , DB , for DH is equal C DB d 36. I. L H M EGF 2 . to DB ; and DF together with CH is the ...
Άλλες εκδόσεις - Προβολή όλων
The First Six Books: Together with the Eleventh and Twelfth Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe centre circle ABCD circumference cone confequently cylinder defcribed demonftrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fide BC fides fimilar firft firſt folid angle fome fore fphere fquare of AC ftraight line AB ftraight line BC given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs likewife oppofite parallel parallelepipeds parallelogram perpendicular plane angles prifms PROP propofition pyramid ratio of BC rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC wherefore
Δημοφιλή αποσπάσματα
Σελίδα 472 - 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.