The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 1
... ALSO THE BOOK OF EUCLID'S DATA , In like manner corrected . BY ROBERT SIMSON , M. D. meritus Profeffor of Mathematics in the University of Glasgow . To this SIXTH EDITION are also annexed , LEMENTS of PLAIN and SPHERICAL TRIGONOMETRY ...
... ALSO THE BOOK OF EUCLID'S DATA , In like manner corrected . BY ROBERT SIMSON , M. D. meritus Profeffor of Mathematics in the University of Glasgow . To this SIXTH EDITION are also annexed , LEMENTS of PLAIN and SPHERICAL TRIGONOMETRY ...
Σελίδα 26
... also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal to the angle CEF , be- cause they are oppofite ver- tical angles ; therefore the bafe AB ...
... also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal to the angle CEF , be- cause they are oppofite ver- tical angles ; therefore the bafe AB ...
Σελίδα 27
... 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 . Let ABC be a triangle , of which the fide AC is ...
... 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 . Let ABC be a triangle , of which the fide AC is ...
Σελίδα 31
... also greater than the base EF . Of the two fides DE , DF , let DE be the fide which is not greater than the other , and at the point D , in the straight line DE , make the angle EDG equal to the angle BAC ; and make a . 23. I. DG equal ...
... also greater than the base EF . Of the two fides DE , DF , let DE be the fide which is not greater than the other , and at the point D , in the straight line DE , make the angle EDG equal to the angle BAC ; and make a . 23. I. DG equal ...
Σελίδα 33
... also the B third angle BAC to the third Edf . D HC E For , if BC be not equal to EF , let BC be the greater of them , and make BH equal to EF , and join AH ; and because BH is equal to EF , and AB to DE ; the two AB , BH are equal to ...
... also the B third angle BAC to the third Edf . D HC E For , if BC be not equal to EF , let BC be the greater of them , and make BH equal to EF , and join AH ; and because BH is equal to EF , and AB to DE ; the two AB , BH are equal to ...
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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.