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

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Side 16

**Wherefore**from the given point A a ftraight line AL has been drawn equal to the given Atraight line BC . Which was to be done . a . 2. I. F 1 PROP . III . PROB . ROM the greater of two given ftraight lines to cut off a part equal to the ... Side 17

**Wherefore**the whole triangle ABC fhall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one fhall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the ... Side 21

I. cides with the base EF , the fides BA , AC cannot but coincide with the fides ED , DF ;

I. cides with the base EF , the fides BA , AC cannot but coincide with the fides ED , DF ;

**wherefore**likewife the angle BAC coincides with the angle EDF , and is equal to it . There . b . s . Ax • fore if two triangles , & c . Side 25

**Wherefore**, if at a point , & c . Q. E. D. PROP . XV . 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 ... Side 33

... and the other angles to the other angles , each to each , to which the equal fides are oppofite ; therefore the angle GCB is equal to the angle DFE ; but DFE is , by the hypothefis , equal to the angle BCA ;

... and the other angles to the other angles , each to each , to which the equal fides are oppofite ; therefore the angle GCB is equal to the angle DFE ; but DFE is , by the hypothefis , equal to the angle BCA ;

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The First Six Books: Together with the Eleventh and Twelfth Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

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

### Populære avsnitt

Side 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.

Side 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.

Side 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...

Side 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.

Side 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.

Side 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.

Side 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.

Side 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...

Side 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...

Side 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.