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" 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 164
by John Keill - 1723 - 364 pages
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...the triangle 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 BC has to EF. Therefore...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 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 also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...BG, so is the triangle ABC to ABG. Therefore (V. 11) the triangle ABC has to ABG the duplicate ratio of that which BC has to EF. But the triangle ABG is equal to DEF ; wherefore also the triangle ABC has to DEF the duplicate ratio of that which BC has to EF.f Therefore,...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 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 also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 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 also the triangle abc has to the triangle def the duplicate ratio of that which bc has...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 pages
...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 also the triangle ABC has to the triangle DEF the duplicate ratio of that which. BC has...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...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 also the triangle ABC has to the triangle DBF the duplicate ratio of that which BC has...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...triangle ABG (VI. 1). Therefore the triangle ABC is to the triangle ABG in the duplicate ratio of BC to EF. But the triangle ABG is equal to the triangle DEF; wherefore also the triangle ABC is to the triangle DEF in the duplicate ratio of BC to EF. COR. —...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...the triangle.4-BC?; (VI.l.) 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 .BClias to EF. Therefore...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...the triangle 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 BC has to EF. Therefore,...
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