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

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Page 313

litude of

litude of

**ratios**, is of the fame kind , and can ferve for no Book V. " purpose in mathematics , but only to give ... definition of the**ratio**" of numbers ; tho ' fuch a definition was as neceffary and ufe- ful to be**given**in that book ... Page 320

Here it is faid , that " A " would have a lefs

Here it is faid , that " A " would have a lefs

**ratio**to C , than B has to C , " or , which is the fame thing , that B ... or Euclid had**given**, has been deceived in applying what is manifeft , when underftood of magnitudes , unto**ratios**... Page 329

and of the

and of the

**ratio**of L to M. " This definition therefore of Book VL Theon is quite ufelefs and abfurd : For that Theon ... have been made after the fame manner in which the definitions of duplicate and triplicate**ratio**are**given**, viz . Page 330

Book VI . is contained in the roth definition of the 5th book , viz . the definition of duplicate

Book VI . is contained in the roth definition of the 5th book , viz . the definition of duplicate

**ratio**, or to be underftood from it , to wit , in the fame manner as Clavius has explained ... 5. book 6. and the explication**given**of it ... Page 332

... that is , of find- ing the ratio of the parallelograms , is fhewn in that , but not in Candalla's demonftration ; whereby beginners may learn , in like cafes , how to find the ratio which is compounded of two or more

... that is , of find- ing the ratio of the parallelograms , is fhewn in that , but not in Candalla's demonftration ; whereby beginners may learn , in like cafes , how to find the ratio which is compounded of two or more

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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.