The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Page 104
Dividendo , by division ; when there are four proportionals , and it is inferred , that the excess of the first above the second , is to the second , as the excess of the third above the fourth , is to the fourth . 17th Prop . Book 5 .
Dividendo , by division ; when there are four proportionals , and it is inferred , that the excess of the first above the second , is to the second , as the excess of the third above the fourth , is to the fourth . 17th Prop . Book 5 .
Page 124
If four magnitudes be proportionals , they are also proportionals by conversion : that is , the first is to its excess above the second , as the third to its excess above the fourth . Let AB be to BE , as CD to DF : then BA shall be to ...
If four magnitudes be proportionals , they are also proportionals by conversion : that is , the first is to its excess above the second , as the third to its excess above the fourth . Let AB be to BE , as CD to DF : then BA shall be to ...
Page 128
If the same hypothesis be made as in the proposition , the excess of the first and fifth shall be to the second , as the excess of the third and sixth to the fourth . The demonstration of this is the same with that of the proposition ...
If the same hypothesis be made as in the proposition , the excess of the first and fifth shall be to the second , as the excess of the third and sixth to the fourth . The demonstration of this is the same with that of the proposition ...
Page 162
... C. Make * the parallelogram KLMN equal to the excess of EF above C , and similar and similarly situated to D : then , since D is similar + to EF , therefore * also KM is similar to EF : let KL be the homologous side to EG , с # 26.
... C. Make * the parallelogram KLMN equal to the excess of EF above C , and similar and similarly situated to D : then , since D is similar + to EF , therefore * also KM is similar to EF : let KL be the homologous side to EG , с # 26.
Page 163
Let AB be the given straight line , and C the given rectilineal figure to which the parallelogram to be applied is required to be equal , and D the parallelogram to which the excess of the one to be applied above that upon the given ...
Let AB be the given straight line , and C the given rectilineal figure to which the parallelogram to be applied is required to be equal , and D the parallelogram to which the excess of the one to be applied above that upon the given ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |
Common terms and phrases
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