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" If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines... "
The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... - Page 42
by Euclid, James Williamson - 1781 - 309 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1762 - 488 pages
...lines be proportionals, the rectangle ^ contained by the extremes is equal to the fquare of' the mean: and if the rectangle contained by the extremes be equal to the fquare of the mean, the three ftraigho lines are proportionals. Let the three ftraight lines A, B,...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 534 pages
...lines be proportionals, the rectangle contained by the extremes is equal to the fquare of fhe mean : And if the rectangle contained by the extremes be equal to the fquare of the mean, the three flraight lines are proportionals. Let the three ftraight lines A, B,...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1781 - 534 pages
...r.• angle ADE. Therefore equal triangles, &c. Q^. ED Book V7. »>, ?, ji-. i4' e PROP. XVI. THE ORIF four ftraight lines be proportionals, the rectangle...rectangle contained by the extremes be equal to the reclangle contained by the means, the four ftraight lines are proportionals. • Let the four ftraight...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 pages
...four ftraight lines he proportionals, the reflangle contained by the extremes is equal to the re&angle contained by the means : And if the rectangle contained...to the rectangle contained by the means, the four ftrargbt lines are proportionals. Let the four ftraight lines, AB, CD, E, F be proportionals, viz....
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - Trigonometry - 1799 - 374 pages
...lines be proportionals, the reftangle contained by the extremes is equal to the fquare of the mean : And if the rectangle contained by the extremes be equal to the fquare of the mean, the three ftraight lines are proportionals. Let the three ftraight lines A, B,...
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair, Euclid - Circle-squaring - 1804 - 468 pages
...lines be proportionals, the reflangle contained by the extremes is equal to the fquarc of the mean : And if the rectangle contained by the extremes be equal to the fquare of the mean, the three ftraight lines are proportionals. ' Let the three ftraight lines A, B,...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804 - 530 pages
...lines be proportionals, the re&angle contained by the extremes is equal to the fquare of the mean : and if the rectangle contained by the extremes be equal to the fquare of the mean, the three ftraight lines arc proportionals. Let the three ftraight lines A, B,...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...9. 4. t? the triangle ADE. Therefore, equal triangles, &c. QE D, PROP. XVI. THEOR. IF four straight lines be proportionals, the rectangle contained by...to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines AB, CD, E, F be proportionals, viz. as...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...Therefore, equal triangles, &c. QED PROP. XVI. THEOR. *•* *f* IF four straight lines be proportional, the rectangle contained by the extremes is equal to...to the rectangle contained by the means, the four straight lines are proportional. Let the four straight lines AB, CD, E, F be proportional, AB to CD...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...proportional, are equal to one 'an. other. Prop. XVI. Theor. If .four straight lines be pro. portionals, I he rectangle contained by the extremes is equal to the...to the rectangle contained by the means, the four straight lines are proportionals. Prop. XVII. Theor. If three straight lines be proportionals, the...
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