The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 17
... base BC fhall be equal to the bafe EF and the triangle ABC to the triangle DEF ; and the other angles , to which the ... base BC fhall coincide with the base EF , because the point B coinciding with E , and C with F , if the bafe BC does ...
... base BC fhall be equal to the bafe EF and the triangle ABC to the triangle DEF ; and the other angles , to which the ... base BC fhall coincide with the base EF , because the point B coinciding with E , and C with F , if the bafe BC does ...
Σελίδα 18
... base of the triangle ABC : And it has alfo been proved that the angle FBC is equal to the angle GCB , which are the angles upon the o- ther fide of the bafe . Therefore the angies at the bafe , & c . Q E. D. COROLLARY . Hence every ...
... base of the triangle ABC : And it has alfo been proved that the angle FBC is equal to the angle GCB , which are the angles upon the o- ther fide of the bafe . Therefore the angies at the bafe , & c . Q E. D. COROLLARY . Hence every ...
Σελίδα 20
... base CD are equal to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is like- wife greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , becaufe CB is equal A to ...
... base CD are equal to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is like- wife greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , becaufe CB is equal A to ...
Σελίδα 21
... base equal to one another , and likewise their fides terminated in the other extre- mity : But this is impoffible ; therefore , if the bafe BC coin- 2 7. I. cides with the base EF , the fides BA , AC cannot but coincide with the fides ...
... base equal to one another , and likewise their fides terminated in the other extre- mity : But this is impoffible ; therefore , if the bafe BC coin- 2 7. I. cides with the base EF , the fides BA , AC cannot but coincide with the fides ...
Σελίδα 31
... base BC is 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 ...
... base BC is 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 ...
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
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.