The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 16
... greater of two given ftraight lines to cut off a part equal to the less . Let AB and C be the two gi ven ftraight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C the lefs . 2 From ...
... greater of two given ftraight lines to cut off a part equal to the less . Let AB and C be the two gi ven ftraight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C the lefs . 2 From ...
Σελίδα 19
... greater than a the other : Let AB be the greater , and from it cut off DB e a 3. I. qual to AC , the lefs , and join DC ; there- fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB ...
... greater than a the other : Let AB be the greater , and from it cut off DB e a 3. I. qual to AC , the lefs , and join DC ; there- fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB ...
Σελίδα 20
... greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , becaufe CB is equal A to DB , the angle BDC is equal to the angle BCD ; but BDC has been proved to be greater than the fame BCD ; which is ...
... greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , becaufe CB is equal A to DB , the angle BDC is equal to the angle BCD ; but BDC has been proved to be greater than the fame BCD ; which is ...
Σελίδα 26
... greater than the angle ECF ; therefore the angle ACD is greater than BAE : In the fame manner , if the fide BC be bifected , it may be demonstrated that the angle BCG , that is d , the angle ACD , is greater than the angle ABC ...
... greater than the angle ECF ; therefore the angle ACD is greater than BAE : In the fame manner , if the fide BC be bifected , it may be demonstrated that the angle BCG , that is d , the angle ACD , is greater than the angle ABC ...
Σελίδα 27
... greater than the angles ABC , ACB ; but ACD , ACB are to- gether equal b to two right angles ; therefore the angles ... greater fide of every triangle is oppofite to the T greater angle . Let ABC be a triangle , of which the fide AC is ...
... greater than the angles ABC , ACB ; but ACD , ACB are to- gether equal b to two right angles ; therefore the angles ... greater fide of every triangle is oppofite to the T greater angle . Let ABC be a triangle , of which the fide AC is ...
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.