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" IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Σελίδα 132
των Euclid, John Playfair - 1853 - 317 σελίδες
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 σελίδες
...CD, fo E to F. Wherefore -'• 14 »• if four, &c. Q._E. D. PROP. XVII. THEOR. TF three ftraight 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...

The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 σελίδες
...therefore AB is to CD, fo E to F. Wherefore, if four, &c. D. PROP. XVII. THEO R. TF three ftraight 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...

The Elements of Euclid: With Dissertations Intended to Assist and Encourage ...

Euclid, James Williamson - 1781 - 309 σελίδες
...are reciprocally proportional, are equal. Which was to be demonftrated. PROP. XVI. If four ftraight 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...

The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 σελίδες
...therefore AB is to CD, fo E to F. Wherefore, if four, &c. D. PROP. XVII. THEO R. }F three ftraight lines be proportionals, the rectangle contained by the extremes is equal to the fquare of the mean : And if the rectangle contained by the extrenies be equal to the fquare of...

The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 σελίδες
...triangle ADE. Therefore equal triangles, &.c. Q^ED c i.6. e 9. 5. PROP. XVI. THEOR. IF four flraight lines be proportionals, the recT:angle contained by the extremes is equal to the rectangle contained by the means : And if the reelangle contained by the extremes be equal to therectangle...

Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1804 - 440 σελίδες
...to D ; A is a to B, as D to C : but if four » ?.V5. llraight lines be proportionals, the reftangle contained by the extremes is equal to that which is contained by the means b : therefore A.— — — ' b ><>. 6. the reftangle AC — the reftangle BD -, but the reftangle...

The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
...ADE. Therefore equal triangles, &c. Q^ED *. ii. i. t. 7. C. 14. 6. PROP. XVI. THEOR. IF four ftraight 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...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 σελίδες
...ABC is equal* e 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 the extremes is equal to the rectangle contained by the means : and if the rectangle contained by the extremes be equal to the...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 σελίδες
...to D ; A isa to B, as D to C : but if four straight lines * 7. 5. be proportionals,the rectA B angle contained by the extremes is equal to that •which is contained by the Dmcans^ : therefore the C , . ,. .. , t, Id. C. rectangle contained by A, C is equal to that contained...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813
...rectangle contained by the means, the four straight lines are proportionals. Prop. XVII. Theor. If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : and if between the dividing line and the extremities of the rectangle contained...




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