The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 6
... fimilar folid Figures are thofe which are contained by " fimilar Planes of the fame Number and Magnitude . " Now , this Propofition is a Theorem , not a Definition ; because the equality of Figures of any kind muft be demonftrated , and ...
... fimilar folid Figures are thofe which are contained by " fimilar Planes of the fame Number and Magnitude . " Now , this Propofition is a Theorem , not a Definition ; because the equality of Figures of any kind muft be demonftrated , and ...
Σελίδα 87
... fimilar to the fegment ADB , and that fimilar fegments of circles contain equal an- br . def . 3 . gles ; the angle ACB is equal to the angle ADB , the exterior A B с to the interior , which is impoffible . Therefore , there cannot e 16 ...
... fimilar to the fegment ADB , and that fimilar fegments of circles contain equal an- br . def . 3 . gles ; the angle ACB is equal to the angle ADB , the exterior A B с to the interior , which is impoffible . Therefore , there cannot e 16 ...
Σελίδα 88
... fimilar PROP . XXV . PROB . Segment of a circle being given , to defcribe the circle of which it is the fegment . Let ABC be the given fegment of a circle ; it is required to defcribe the circle of which it is the fegment . Bifect AC in ...
... fimilar PROP . XXV . PROB . Segment of a circle being given , to defcribe the circle of which it is the fegment . Let ABC be the given fegment of a circle ; it is required to defcribe the circle of which it is the fegment . Bifect AC in ...
Σελίδα 89
... fimilar to the bII . def.3 . fegment EDF ; and they are upon equal ftraight lines BC , EF ; but fimilar fegments of circles upon equal ftraight lines are e- qual to one another ; therefore the fegment BAC is equal 24.3 . to the fegment ...
... fimilar to the bII . def.3 . fegment EDF ; and they are upon equal ftraight lines BC , EF ; but fimilar fegments of circles upon equal ftraight lines are e- qual to one another ; therefore the fegment BAC is equal 24.3 . to the fegment ...
Σελίδα 166
... fimilar : In the like b 4. 6 . D C manner it may be demonftrated , that the triangle ADC is e quiangular and fimilar to the triangle ABC : And the triangles ABD , ADC , being both equiangular and fimilar to ABC , are equiangular and fimilar ...
... fimilar : In the like b 4. 6 . D C manner it may be demonftrated , that the triangle ADC is e quiangular and fimilar to the triangle ABC : And the triangles ABD , ADC , being both equiangular and fimilar to ABC , are equiangular and fimilar ...
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.