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

### Inni boken

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Side 5

... especially in the Fifth and Eleventh

... especially in the Fifth and Eleventh

**Books**of the Elements , which this Editor has greatly vitiated ; for instance , by fubftituting a fhorter , but infufficient Demonftration of the 18th Prop . of the 5th**Book**, in place of the ... Side 6

5th

5th

**Book**, by which the Doctrine of Compound Ratios is ren dered plain and eafy . Befides , among the Definitions of the 11th**Book**, there is this , which is the 10th , viz . " Equal " and fimilar folid Figures are thofe which are ... Side 7

Mathematical Learning , to remove fuch Blemishes , and re- flore the principal

Mathematical Learning , to remove fuch Blemishes , and re- flore the principal

**Books**of the Elements to their original Ac- curacy , as far as I was able ; efpecially fince thefe Elements are the Foundation of a Science by which the ... Side 21

BC is equal to EF ; therefore BC coinciding with EF , BA and

BC is equal to EF ; therefore BC coinciding with EF , BA and

**Book**1 . AC fhall coincide with ED and DF ; for , if the bafe BC cain- cides with the bafe EF , but the fides BA , CA do not coin- cide with the fides ED , FD , but have a ... Side 23

It is required to draw a straight line perpendicular to AB from the point C. Take any point D upon the other fide of AB , and from the centre C , at the distance CD , defcribe the circle EGF C a

It is required to draw a straight line perpendicular to AB from the point C. Take any point D upon the other fide of AB , and from the centre C , at the distance CD , defcribe the circle EGF C a

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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.