The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 17
... remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two tri- angles have two fides of the one equal to two fides of the other , each to each , and have ...
... remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two tri- angles have two fides of the one equal to two fides of the other , each to each , and have ...
Σελίδα 18
... remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal fides are oppofite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB : And because the whole AF is ...
... remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal fides are oppofite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB : And because the whole AF is ...
Σελίδα 25
... remaining angle ABE is equal to the remaining b 3. Ax . angle ABD , the lefs to the greater , which is impoffible ; there fore BE is not in the fame ftraight line with BC . And , in like manner , it may be demonftrated , that no other ...
... remaining angle ABE is equal to the remaining b 3. Ax . angle ABD , the lefs to the greater , which is impoffible ; there fore BE is not in the fame ftraight line with BC . And , in like manner , it may be demonftrated , that no other ...
Σελίδα 26
... remaining angles to the remaining angles , each to each , to which the equal fides are oppofite ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD is greater than the angle ECF ; therefore the angle ACD is greater ...
... remaining angles to the remaining angles , each to each , to which the equal fides are oppofite ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD is greater than the angle ECF ; therefore the angle ACD is greater ...
Σελίδα 35
... remaining angle AGH is equal to the re- maining angle GHD ; and they are alternate angles ; there- fore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. IF PROP . XXIX . THEOR . a ftraight line falls upon two ...
... remaining angle AGH is equal to the re- maining angle GHD ; and they are alternate angles ; there- fore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. IF PROP . XXIX . THEOR . a ftraight line falls upon two ...
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.