## The First Six Books: Together with the Eleventh and Twelfth |

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Page 16

THEOREM . two triangles have two fides of the one equal to two fides of the other , each to each ; and have likewise the angles contained by thofe fides equal to one another ; they fhall likewife have their bafes , or

THEOREM . two triangles have two fides of the one equal to two fides of the other , each to each ; and have likewise the angles contained by thofe fides equal to one another ; they fhall likewife have their bafes , or

**third**fides ... Page 28

Let ABC be a triangle ; any two fides of it together are greater than the

Let ABC be a triangle ; any two fides of it together are greater than the

**third**fide , viz . the fides BA , AC greater than the fide BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to the point D , and make ... Page 29

Let A , B , C be the three given ftraight lines , of which any two whatever are greater than the

Let A , B , C be the three given ftraight lines , of which any two whatever are greater than the

**third**, viz . A and B greater than C ; A and C greater than B ; and B and C than A. It is required to make a triangle of which the fides ... Page 32

ABG to DE , and AC to DF ; and the

ABG to DE , and AC to DF ; and the

**third**angle BAC to the**third**angle EDF . For , if AB be not D equal to DE , one of B them must be the с E F 1 greater . Let AB be the greater of the two , and make BG equal to DE , and join GC ... Page 33

... therefore the two AB , BC are equal to the two DE , EF , each to each ; and the angle ABC is equal to the angle DEF ; the base therefore AC is equal to the base DF , and the

... therefore the two AB , BC are equal to the two DE , EF , each to each ; and the angle ABC is equal to the angle DEF ; the base therefore AC is equal to the base DF , and the

**third**angle BAC to the**third**angle EDF .### What people are saying - Write a review

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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.