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

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Page 1

The Errors , by which THEON , or others , have long ago vitiated

The Errors , by which THEON , or others , have long ago vitiated

**these**Books , are corrected , And fome of EUCLID'S Demonftrations are reftored . ALSO THE BOOK OF EUCLID'S DATA , In like manner corrected . Page 7

... or others have fuppreffed , and which have

... or others have fuppreffed , and which have

**these**many ages been buried in Oblivion . In this Sixth Edition , Ptolemy's Propofition concerning a Pro- perty of quadrilateral Figures in a Circle is added at the End of the fixth Book . Page 10

... at the point in which the ftraight lines that contain the angle meet one another , is put between the other two letters , and one of

... at the point in which the ftraight lines that contain the angle meet one another , is put between the other two letters , and one of

**these**two is fomewhere upon one of thofe ftraight lines , and the other upon the other line : Thus ... Page 12

ᄆᄆ XXXIII . See N. A rhomboid , is that which has its oppofite fides equal to one another , but all its fides are not equal , nor its angles right angles . XXXIV . All other four fided figures befides

ᄆᄆ XXXIII . See N. A rhomboid , is that which has its oppofite fides equal to one another , but all its fides are not equal , nor its angles right angles . XXXIV . All other four fided figures befides

**these**, XIV 12 THE ELEMENTS An ... Page 13

All other four fided figures befides

All other four fided figures befides

**these**, are called Trapeziums . XXXV . Parallel ftraight lines , are fuch as are in the fame plane , and which , being produced ever so far both ways , do not meet . Book I. POSTULATES .### 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.