The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 16
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the fame are equal to one another ; therefore the ftraight line AL is equal to BC . Wherefore from the given point A a ftraight line AL has been drawn equal ...
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the fame are equal to one another ; therefore the ftraight line AL is equal to BC . Wherefore from the given point A a ftraight line AL has been drawn equal ...
Σελίδα 17
... wherefore alfo the point C fhall coincide with the point F , because the ftraight line AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC fhall coincide with the base EF , because the point B ...
... wherefore alfo the point C fhall coincide with the point F , because the ftraight line AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC fhall coincide with the base EF , because the point B ...
Σελίδα 21
... wherefore likewife the angle BAC coincides with the angle EDF , and is equal to it . There . b . s . Ax • fore if two triangles , & c . Q. E. D. T PROP . IX . PROB . O bisect a given rectilineal angle , that is , to divide it into two ...
... wherefore likewife the angle BAC coincides with the angle EDF , and is equal to it . There . b . s . Ax • fore if two triangles , & c . Q. E. D. T PROP . IX . PROB . O bisect a given rectilineal angle , that is , to divide it into two ...
Σελίδα 25
... Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR . IF two ftraight lines cut one another , the vertical , or op- pofite , angles fhall be equal . Let the two ftraight lines AB , CD cut one another in the point E ; the angle ...
... Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR . IF two ftraight lines cut one another , the vertical , or op- pofite , angles fhall be equal . Let the two ftraight lines AB , CD cut one another in the point E ; the angle ...
Σελίδα 33
... wherefore alfo the angle BCG is equal to the angle BCA , the lefs to the greater , which is impoffible ; therefore ... wherefore BC is not unequal to EF , that is , b 16. 1 . it is equal to it ; and AB is equal to DE ; therefore the two ...
... wherefore alfo the angle BCG is equal to the angle BCA , the lefs to the greater , which is impoffible ; therefore ... wherefore BC is not unequal to EF , that is , b 16. 1 . it is equal to it ; and AB is equal to DE ; therefore the 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.