The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 σελίδες |
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Σελίδα 18
... THEOR . F two angles of a triangle be equal to one another , the fides alfo which fubtend , or are oppofite to , the equal angles , fhall be equal to one another . Let 1 Let ABC be a triangle having the angle ABC 18 THE ELEMENTS.
... THEOR . F two angles of a triangle be equal to one another , the fides alfo which fubtend , or are oppofite to , the equal angles , fhall be equal to one another . Let 1 Let ABC be a triangle having the angle ABC 18 THE ELEMENTS.
Σελίδα 19
... THEOR . 4 . PON the fame bafe , and on the fame fide of it , See N. there cannot be two triangles that have their fides which are terminated in one extremity of the bafe equal to one another , and likewife those which are terminated in ...
... THEOR . 4 . PON the fame bafe , and on the fame fide of it , See N. there cannot be two triangles that have their fides which are terminated in one extremity of the bafe equal to one another , and likewife those which are terminated in ...
Σελίδα 20
... THEOR . F two triangles have two fides of the one equal to two fides of the other , each to each , and have like wife their bafes equal ; the angle which is contained by the two fides of the one fhall be equal to the angle con tained by ...
... THEOR . F two triangles have two fides of the one equal to two fides of the other , each to each , and have like wife their bafes equal ; the angle which is contained by the two fides of the one fhall be equal to the angle con tained by ...
Σελίδα 23
... THEOR . HE angles which one ftraight line makes with an- other upon the one fide of it , are either two right THE angles , or are together equal to two right angles . B 4 Let Book I. Let the ftraight line AB make with CD OF EUCLID . 23.
... THEOR . HE angles which one ftraight line makes with an- other upon the one fide of it , are either two right THE angles , or are together equal to two right angles . B 4 Let Book I. Let the ftraight line AB make with CD OF EUCLID . 23.
Σελίδα 25
... 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 AEC fhall be equal to the angle DEB , and CEB to ALD ...
... 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 AEC fhall be equal to the angle DEB , and CEB to ALD ...
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.