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Books Books 1 - 10 of 32 on ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio....  
" ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which... "
Euclid's Elements of geometry: from the Latin translation of Commandine. To ... - Page 168
by John Keill - 1723 - 364 pages
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Euclid's Elements of geometry: from the Latin translation of Commandine. To ...

John Keill - Trigonometry - 1733 - 397 pages
...as EF is to BG, and if three Right Lines * Dtf. 10. 5. be proportional, the firft has * a duplicate Proportion to the third, of what it has to the fecond....a duplicate Proportion of that which BC has to EF ; arid as BC is to BG, fo is the Triangle ABC to the Triangle ABG, whence the Triangle ABC bears to...
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The Elements of Euclid: The errors, by which Theon, or others, have long ago ...

Robert Simson, Euclid - Trigonometry - 1762 - 466 pages
...triangle ABC to the triangle ABG. therefore the triangle ABC has to the triangle ABG, the duplicate ratio of that which BC has to EF. but the triangle ABG is equal to the irhngle DEF ; wherefore alfq the triangle ABC has to the triangle DEF the duplicate ratio of that which...
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The Elements of Euclid, viz: The errors, by which Theon, or others, have ...

Robert Simson, Euclid - Trigonometry - 1775 - 520 pages
...triangle ABC to the triangle ABG. Therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: But the triangle ABG is equal to the triangle DEF; wherefore alfo the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to...
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The elements of Euclid: with dissertations intended to assist and ..., Volume 1

James Williamson - Mathematics - 1781
...ABC to the triangle ABG: therefore alfo the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF : but the triangle ABG is, equal to the triangle DEF; therefore (by 7. 5.) the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has, to EF....
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1781 - 466 pages
...triangle ABC to the triangle ABG. therefore the triangle ABC has to the triangle ABG, the duplicate ratio of that which BC has to EF. but the triangle ABG is equal to the triangle DEF ; wherefore allb the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 pages
...triangle ABG. Therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC rus to EF : But the triangle ABG is equal to the triangle DEF; wherefore alfo the triangle ABC has to the triangle DEF the duplicate ratfo of that which BC has to...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - Euclid's Elements - 1795 - 400 pages
...triangle ABC to the triangle ABG. Therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF : but the triangle ABG is equal to the triangle DEF ; wherefore alfo the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has...
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The elements of Euclid: viz. the first six books, with the eleventh and ...

Trigonometry - 1799 - 351 pages
...triangle ABC to the triangle ABG. Therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF : But the triangle ABG is equal to the triangle DEF ; wherefore alfo the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...triangle ABC to the triangle ABG. Therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF : But the triangle ABG is equal to the triangle DKF: Wherefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...triangle ABG. Therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC hat to EF : But the triangle ABG is equal to the triangle DEF ; wherefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC bas...
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