The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 17
... bafe EF and the triangle ABC to the triangle DEF ; and the other angles , to which the equal fides are oppofite ... bafe BC does not coincide with the bafe EF , two ftraight lines would inclofe a fpace , which is impoffible . Therefore a ...
... bafe EF and the triangle ABC to the triangle DEF ; and the other angles , to which the equal fides are oppofite ... bafe BC does not coincide with the bafe EF , two ftraight lines would inclofe a fpace , which is impoffible . Therefore a ...
Σελίδα 18
... bafe FC is e- qual to the bafe GB , and the tri- angle AFC to the triangle AGB ; and the 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 ...
... bafe FC is e- qual to the bafe GB , and the tri- angle AFC to the triangle AGB ; and the 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 ...
Σελίδα 19
... bafe DC is equal to the bafe AB , and the triangle DBC is equal to the triangleb ACB , the lefs to the greater ; which is abfurd . Therefore B AB is not unequal to AC , that is , it is A D equal to it . Wherefore , if two angles , & c ...
... bafe DC is equal to the bafe AB , and the triangle DBC is equal to the triangleb ACB , the lefs to the greater ; which is abfurd . Therefore B AB is not unequal to AC , that is , it is A D equal to it . Wherefore , if two angles , & c ...
Σελίδα 20
... bafe equal to one another , and likewife thofe which are terminated in the other extremity . Q. E. D. IF PROP . VIII ... bafe BC equal to the bafe EF . The angle BAC is e- qual to the angle EDF . For , if the tri- DG angle ABC be ap- B ...
... bafe equal to one another , and likewife thofe which are terminated in the other extremity . Q. E. D. IF PROP . VIII ... bafe BC equal to the bafe EF . The angle BAC is e- qual to the angle EDF . For , if the tri- DG angle ABC be ap- B ...
Σελίδα 21
... bafe BC cain- cides with the bafe EF , but the fides BA , CA do not coin- cide with the fides ED , FD , but have a different fituation , as EG , FG ; then , upon the fame bafe EF , and upon the fame fide of it , there can be two ...
... bafe BC cain- cides with the bafe EF , but the fides BA , CA do not coin- cide with the fides ED , FD , but have a different fituation , as EG , FG ; then , upon the fame bafe EF , and upon the fame fide of it , there can be 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.