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" Parallelograms on the same base and between the same parallels are equal to one another. "
University local half-hour examination papers - Σελίδα 56
των John Robertson (LL.D., of Upton Park sch.) - 1882
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

The Popular Educator, Τόμοι 1-2;Τόμος 12

1867 - 964 σελίδες
...proceed to show. The reader will remember that in Problem XXIV (page 308) it was shown that triangles on the same base and between the same parallels are equal to one another, and that triangles on equal bases and between the same parallels are also equal to one another. Now...

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

John Playfair - 1806 - 320 σελίδες
...parallelogram ABCD is equal to EFGH. Wherefore, parallelograms, &c. QED PROP. XXXVII. THEOR. TRIANGLES upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DEC be upon the same base BC, and between the same parallels AD, BC; the triangle...

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

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...paralkio c 4. 1. gram ACDB into two equal parts. QED PROP. XXXV. THEOR. See N. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. Sue OH- Let the parallelograms ABCD, EBCF be upon the same base 2dand3d BC, and between the same parallels...

A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton - 1812 - 620 σελίδες
...BC, and also parallel ioit(th. 12). q. ED THEOREM XXV. PARALLELOGRAMS, as also Triangles, standing on the Same Base, and between the Same Parallels, are equal to each other. Let E Let ABCD, ABEP, be two parallelograms, and ABC, ABF, two triangles, standing on the...

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

John Mason Good - 1813 - 714 σελίδες
...basis, and between the same parallels, are equal to one another. Prop. XXXVII. Theor. Triangles npon the 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...

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

Euclides - 1816 - 588 σελίδες
...divides the parallelogram ACDB into two equal" parts. PROP. XXXV. THEOR. , s«eN. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. See the ad Let the parallelograms ABCD, EBCF be upon the same and 3d fi. base BC, and between the same...

Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 σελίδες
...parallelogram ACDB into two equal parts. Therefore, &c. Q, ED PROP. XXXV. THEOR. Parallelogram* upon the same base and between the same parallels, are equal to one another. vi^(sEE THE 2d AND 3d FIGURDS.) Let the parallelograms ABCD, EBCF be upon the same base BC> and between...

Hawney's Complete Measurer: Or, The Whole Art of Measuring: Being a Plain ...

William Hawney - 1820 - 336 σελίδες
...of the wedge be perpendicular to its base ABFB, or inclined as ABI, since parallelopipedons standing on the same base and between the same parallels are equal to each other (Euclid, XI. and 29.) But when the edge CD of the wedge is longer or shorter than the base,...

Transactions of the Cambridge Philosophical Society

Cambridge Philosophical Society - 1842 - 458 σελίδες
...with the first twenty-six propositions of Euclid, and not till then, it becomes evident to him, that parallelograms on the same base and between the same parallels are equal ; and he cannot even conceive the contrary. When he has a little further cultivated his geometrical...

Elementary Illustrations of the Celestial Mechanics of Laplace: Part the ...

Pierre Simon de Marquis Laplace, Thomas Young - 1821 - 372 σελίδες
...DCB (105), and A BC is common, therefore they are equal (102), and AB=CD, and AC=BD. 115. THEOREM. Parallelograms on the same base, and between the same parallels, are equal. ABC __ T> Since AB=CD, botli being cqnal to EF, AC=BD (15, or 16), and the triangle AEC is equiangular...




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