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

### From inside the book

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Page 18

... and the bafe BC is

... and the bafe BC is

**common**to the two triangles BFC , CGB ; wherefore the triangles are equal ' , and their remaining angles , each to each , to which the equal fides are oppofite ; therefore the angle FBC is equal to the angle GCB ... Page 19

I. qual to AC , the lefs , and join DC ; there- fore , because in the triangles DBC , ACB , DB is equal to AC , and BC

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 , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to ... Page 21

Becaufe AD is equal to AE , and AF is

Becaufe AD is equal to AE , and AF is

**common**to the two triangles DAF , EAF ; the two fides DA , ÄƑ , are equal to the two fides EA , AF , each to each ; and the bafe DF is e- B qual to the base EF ; therefore the с angle DAF is equal ... Page 22

I. C Because AC is equal to CB , and CD

I. C Because AC is equal to CB , and CD

**common**to the two triangles ACD , BCD ; the two fides AC , CD are e- qual to BC , CD , each to each ; and the angle ACD is equal to the angle BCD ; therefore the bafe AD is equal to the bafe DB ... Page 23

I. Because FH is equal to HG , and HC

I. Because FH is equal to HG , and HC

**common**to the two triangles FHC , GHC , the two fides FH , HC are equal to the to the d 15. Def . two GH , HC , each to each ; and the bafe CF is equal bafe CG ; therefore the angle CHF is equal to ...### 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.