## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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Page 280

Analogy is the simili6 tude of

Analogy is the simili6 tude of

**ratios**, is of the same kind , and can serve for “ no purpose in mathematics ... such a definition was as necessary and useful s to be**given**in that book as in this : but indeed there “ is scaree any need ... Page 287

B. V. Of this there is

B. V. Of this there is

**given**a more explicit demonstration than that which I found in the Elements . ... have to C a greater**ratio**than B to C : I say " that A is greater than B : for if it be not greater it is “ either equal or less . Page 288

The demonstration we have

The demonstration we have

**given**of the 10th prop . is no doubt the same with that of Eudoxus or Euclid , as it is immediately and directly derived from the definiA С B tion of a greater**ratio**, viz . the 7th of the 5th . Page 296

On these accounts , a demonstration is

On these accounts , a demonstration is

**given**in Euclid's manner , like to that he makes use of in the 20th Prop . of ... than the doctrine of compound**ratio**, which Theon has rendered absurd and ungeometrical by substituting the 5th ... Page 297

Clavius , in his observations upon it , rightly judges that the definition of compound

Clavius , in his observations upon it , rightly judges that the definition of compound

**ratio**might have been made after the same manner in which the definitions of duplicate and triplicate**ratio**are**given**, viz .### What people are saying - Write a review

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |

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added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole