Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
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Σελίδα 142
Because the triangle ABE is similar to the triangle FGL ABE has to FGL the duplicate ratio ( 19. 6. ) of that which the side BE has to the side GL : for the same reason , the triangle BEC has to GLH the duplicate ratio of that which BE ...
Because the triangle ABE is similar to the triangle FGL ABE has to FGL the duplicate ratio ( 19. 6. ) of that which the side BE has to the side GL : for the same reason , the triangle BEC has to GLH the duplicate ratio of that which BE ...
Σελίδα 143
Because all squares are similar figures , the ratio of any two squares to one another is the same with the duplicate ratio of ... also , any two şimilar rectilineal figures are to one another as the squares of their homologous sides .
Because all squares are similar figures , the ratio of any two squares to one another is the same with the duplicate ratio of ... also , any two şimilar rectilineal figures are to one another as the squares of their homologous sides .
Σελίδα 144
8 : . similar rectilineal figures MF , NH , in like manner : the rectilineal figure KAB is to LCD , as MF to NH . To AB , CD take a third proportional ( 11. 6. ) X ; and to EF , GH , a third proportional 0 : and because AB : CD :: EF ...
8 : . similar rectilineal figures MF , NH , in like manner : the rectilineal figure KAB is to LCD , as MF to NH . To AB , CD take a third proportional ( 11. 6. ) X ; and to EF , GH , a third proportional 0 : and because AB : CD :: EF ...
Σελίδα 145
The parallelograms about the diameter of any parallelogram , are similar to the whole , and to one another . > Let ABCD be a parallelogram , of which the diameter is AC ; and EG , HK the parallelograms about the diameter : the ...
The parallelograms about the diameter of any parallelogram , are similar to the whole , and to one another . > Let ABCD be a parallelogram , of which the diameter is AC ; and EG , HK the parallelograms about the diameter : the ...
Σελίδα 146
to AD , as AE to AG ; and DC to CB , as GF to FE ; and also CD to DA , as FG to GA : therefore the sides of the parallelo DK C grams ABCD , AEFG about the equal angles are proportionals ; and they are therefore similar to one another ...
to AD , as AE to AG ; and DC to CB , as GF to FE ; and also CD to DA , as FG to GA : therefore the sides of the parallelo DK C grams ABCD , AEFG about the equal angles are proportionals ; and they are therefore similar to one another ...
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ABC is equal ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior angle extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
| Συγγραφέας | John Playfair |
| Εκδότης | E. Duyckinck, and George Long, 1824 |
| Πρωτότυπο από | Πανεπιστήμιο της Ιντιάνα |
| Ψηφιοποιήθηκε στις | 15 Ιαν. 2009 |
| Μέγεθος | 333 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |