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" Triangles upon equal bases, and between the same parallels, are equal to one another. "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 26
by Dennis M'Curdy - 1846 - 138 pages
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The Popular Educator, Volumes 1-2; Volume 12

Geography - 1867
...any point in tho straight line HK, produced both ways indefinitely. Triangles also which stand npon equal bases and between the same parallels are equal to one another. Thus, the triangles LNG, M o F, which „ ._ stand on equal bases, NG, F o, and K between the same...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...ABC is'equal to the triangle DBC. Wherefore, triangles, fee, QE D, PROP. XXXVIII. THEOR. TRIANGLES upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF, AD : the triangle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...Ax. ABC is equald to the triangle DBC. Wherefore, triangles, &c. QED PROP. XXXVIII. THEOR. TRIANGLES upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF, AD ; the triangle...
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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1806 - 452 pages
...ABCD being a parallelogram, AB will be=CD and AD = BC, THEOREM XIII, All parallelograms on the same or equal bases and between the same parallels, are equal to one ' another, that is, if BD^GH, and the lines BH and AF parallel, then the parallel0gram ABDC ^BDFE=EFHG. .fig....
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A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 440 pages
...ABCD being a parallelogram, AB will be=CD and AD=BC. THEO. XIII. All parallelograms on the same or equal bases and between the same parallels, are equal to one another, that is, ifBD=GH, and the lines Ell and AY parallel, then the parallelogram ABDC=BDFE=EFHG. fc 31,...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...same base, and between the same parallels, are equal to one another. Prop. XXXVIII. Theor. Triangles upon equal bases, and between the same parallels, are equal to one another. Prop. XXXIX. Theor. Equal triangles upon the same base, and upon the same side of it, are between the...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 558 pages
...Therefore parallelograms upon the same base, &c. QED BooR I. PROP. XXXVI. THEOR. '—v^> PARALLEL0GRAMS upon equal bases, and between the same parallels, are equal to one another. Let ABCD, EFGH.be _. equal to EFGH. L . parallelograms upon e- '— qual bases BC.FG, and between the same parallels...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...parallelogram EBCF. Therefore parallelograms upon the same base, &c. QED 1 PROP. XXXVI. THEOR. Boot I. PARALLELOGRAMS upon equal bases, and between the same parallels, are equal to one another. •f> K LetABCD,EFGH,be parallelograms upon equal bases BC,FG, and between the same parallels AH, BG;...
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A Treatise on Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1818 - 478 pages
...being a parallelogram, AB will be=CD and AD=BC. THEOREM XIII. •All parallelograms on the same or equal bases and between the same parallels, are equal to one another, that is, if BD=GH, and the lines BH and AF parallel, then the parallelogram J1BDC=BDFE=EFHG. /g. 31....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1819 - 333 pages
...triangle ABC is equal to the triangle DBC. Wherefore triangles, &c. Q, ED PROP. XXXVIII. THEOR. Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF, AD : The triangle...
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