The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 1
... these Books , are corrected , And fome of EUCLID'S Demonftrations are reftored . 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 ...
... these Books , are corrected , And fome of EUCLID'S Demonftrations are reftored . 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 ...
Σελίδα 7
... these many ages been buried in Oblivion . In this Sixth Edition , Ptolemy's Propofition concerning a Pro- perty of quadrilateral Figures in a Circle is added at the End of the fixth Book . Alfo the Note on the 29th Prop . Book ift , is ...
... these many ages been buried in Oblivion . In this Sixth Edition , Ptolemy's Propofition concerning a Pro- perty of quadrilateral Figures in a Circle is added at the End of the fixth Book . Alfo the Note on the 29th Prop . Book ift , is ...
Σελίδα 10
... these two is fomewhere upon one of thofe ftraight lines , and the other upon the other line : Thus the angle which is contained by the ftraight lines AB , CB is named the angle ABC , or CBA ' ; that which is contained by AB , DB is ...
... these two is fomewhere upon one of thofe ftraight lines , and the other upon the other line : Thus the angle which is contained by the ftraight lines AB , CB is named the angle ABC , or CBA ' ; that which is contained by AB , DB is ...
Σελίδα 13
... these , are called Trapeziums . XXXV . Parallel ftraight lines , are fuch as are in the fame plane , and which , being produced ever so far both ways , do not meet . Book I. POSTULATES . I. ET it be granted that a straight line may be ...
... these , are called Trapeziums . XXXV . Parallel ftraight lines , are fuch as are in the fame plane , and which , being produced ever so far both ways , do not meet . Book I. POSTULATES . I. ET it be granted that a straight line may be ...
Σελίδα 25
... these angles are toge- ther equal a to two right angles . Again , because the ftraight line DE makes with AB the angles A AED , DEB , these alfo are together equal a to two right angles ; and CEA , AED have been demonftrated to be equal ...
... these angles are toge- ther equal a to two right angles . Again , because the ftraight line DE makes with AB the angles A AED , DEB , these alfo are together equal a to two right angles ; and CEA , AED have been demonftrated to be equal ...
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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.