The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner CorrectedT. Desilver and R. Desilver, 1825 - 516 sider |
Inni boken
Resultat 6-10 av 38
Side 125
... equimultiples whatever ; then E is to B , as F to D. Take of E , F any equimultiples whatever K , L , and of B , Dany equimultiples whatever G , H ; then it may be demon- strated , as before , that K is the same multiple of A , that L ...
... equimultiples whatever ; then E is to B , as F to D. Take of E , F any equimultiples whatever K , L , and of B , Dany equimultiples whatever G , H ; then it may be demon- strated , as before , that K is the same multiple of A , that L ...
Side 126
... equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are either equal to these others , or equimulti- ples of them . * Let the two magnitudes AB , CD be equimultiples of the two E , F ...
... equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are either equal to these others , or equimulti- ples of them . * Let the two magnitudes AB , CD be equimultiples of the two E , F ...
Side 127
... equal , equal ; if less , less . * Take any equimultiples of each of them , as the doubles of each ; then , by def . 5th of this book , if the double of the first be greater than the double of the second , the double of the third is ...
... equal , equal ; if less , less . * Take any equimultiples of each of them , as the doubles of each ; then , by def . 5th of this book , if the double of the first be greater than the double of the second , the double of the third is ...
Side 128
... equimultiples what- ever E and F ; and of B and D any equi- multiples whatever G and H ; then , because A is the same multiple of B that C is of D ; and that E is the same multiple of A , that F is of C ; E is the same multiple of B ...
... equimultiples what- ever E and F ; and of B and D any equi- multiples whatever G and H ; then , because A is the same multiple of B that C is of D ; and that E is the same multiple of A , that F is of C ; E is the same multiple of B ...
Side 129
... equimultiples have been taken E and F ; A is to E , as C to F ( Cor . 4. 5. ) : but A is equal to E , therefore C is ... equimultiples whatever D and E , and See Note . R See the figure at the foot of the preceding page . of C any ...
... equimultiples have been taken E and F ; A is to E , as C to F ( Cor . 4. 5. ) : but A is equal to E , therefore C is ... equimultiples whatever D and E , and See Note . R See the figure at the foot of the preceding page . of C any ...
Andre utgaver - Vis alle
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore