The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 pages |
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Page 367
... given in magni II . can A ratio is faid to be given , when a ratio of a given magnitude to a given magnitude which ... position , and a straight line from it to the circumference is given in magnitude . VII . Segments of circles are faid ...
... given in magni II . can A ratio is faid to be given , when a ratio of a given magnitude to a given magnitude which ... position , and a straight line from it to the circumference is given in magnitude . VII . Segments of circles are faid ...
Page 388
... given in po- fition and magnitude be given ; the other extremity fhall also be given . Let the point A be given , to ... position . PROP . IF PROP . : XXXII . a ftraight line be 388 EUCLI D's.
... given in po- fition and magnitude be given ; the other extremity fhall also be given . Let the point A be given , to ... position . PROP . IF PROP . : XXXII . a ftraight line be 388 EUCLI D's.
Page 390
... position . Let A be a given point , and BC a ftraight line given in pof- tion , a ftraight line given in magnitude drawn from the point A to BC is given in pofition . A E C Because the flraight line ... given point given 390 EUCLID's с ...
... position . Let A be a given point , and BC a ftraight line given in pof- tion , a ftraight line given in magnitude drawn from the point A to BC is given in pofition . A E C Because the flraight line ... given point given 390 EUCLID's с ...
Page 391
... given point A to a ftraight line BC given in position . IF PROP . XXXV . F a ftraight line be drawn between two parallel straight lines given in pofition , and makes given angles with them , the ftraight line is given in magnitude . Let ...
... given point A to a ftraight line BC given in position . IF PROP . XXXV . F a ftraight line be drawn between two parallel straight lines given in pofition , and makes given angles with them , the ftraight line is given in magnitude . Let ...
Page 393
... position , in a given angle EKC ; EK is A F H B 1 € 31. dat . 34 E FH B E C KG D C G K D given in pofition ; and AB , CD are given in pofition ; there- fore the points H , K are given : And ... given point A , let the straight DAT TA . 393.
... position , in a given angle EKC ; EK is A F H B 1 € 31. dat . 34 E FH B E C KG D C G K D given in pofition ; and AB , CD are given in pofition ; there- fore the points H , K are given : And ... given point A , let the straight DAT TA . 393.
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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...
Page 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.