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" IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. "
The synoptical Euclid; being the first four books of Euclid's Elements of ... - Side 53
av Euclides - 1853
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...produced. Let the straight line AB he bisected at C, and produced to the point D. The rectangle AD.DB, together with the square of CB, is equal to the square of C D. Upon CD describe the square CF (I. 46). Join DE. Through B draw BHG parallel to CE or DF (L 31);...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...from D, the middle point of BC, DE is drawn perpendicular to AS: shew that BE is, one-fourth of AB. 5. If a straight line be divided into any two parts, the squares on the whole line and one of the parts, shall be together equal to twice the rectangle contained by...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...line made up of the half and the part produced. Let AB (Fig. 41) be bisected in C, and produced to D. The rectangle AD, DB, together with the square of CB, is equal to the square of C D. Because the line AD is divided into parts at the points C, B, the rectangle AD, BD is equal to...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...unequal segments is equal to the difference between the squares on half the line and the mean distance. If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole...
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The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860
...angles. 5. Parallelograms upon equal bases and between the same parallels are equal to one another. 6. If a straight line be divided into any two parts, the squares on the whole line and one of the parts are equal to twice the rectangle contained by the whole and...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 sider
...CB, together with the square on BC. If therefore a straight line be divided, &c. QED PROPOSITION IV. THEOREM. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 sider
...to it. 2. Triangles upon the same base, and between the same parallels, are equal to one another. 3. If a straight line be divided into any two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1861
...expect to find the " differences " largest at the early part of the table and gradually decreasing. 14. If a straight line be divided into any two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862
...equal to the rectangle AD, DB ; add to each of these LG, which is equal to the square of CB ; therefore the rectangle AD, DB, together with the square of CB. is equal to tin gnomon CMG, and the figure LG; but the gnomon CMG and LG make up the whole figure CEFD, which is...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...and by A and EC. Conclusion. — Therefore, if there be two straight lines, &c. QED PROPOSITION 2.— THEOREM. If a straight line be divided into any two parts, the rectangles contained by the whole line and each of its parts, are together equal to the square on the...
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