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" Parallelograms upon the same base and between the same parallels, are equal to one another. "
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Strona 35
autor: John Playfair - 1855 - Liczba stron: 318
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...divides the parallelogram ACDB into two equal parts. QED PROPOSITION XXXV. THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC. Then the...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - Liczba stron: 199
...ACDB into two equal parts. QED BOOK I. PROP. XXXV. XXXVI. PROPOSITION XXXV. THEOR. — Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same See the 2nd base BC, and between the same parallels AF,...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - Liczba stron: 352
...parallelogram AC is equal (I. ax. 1) to EG. Wherefore parallelograms, &c. PROP. XXXVII. TnEOR.t — Triangles upon the same base, and between the same parallels, are equal to one another. * lt will appear, from this proposition, that the perimeters of two equal parallelograms on the same...
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The London University Calendar

London univ - 1846
...exterior angles of any rectilineal figure are together equal to four right angles. 6. Parallelograms upon the same base and between the same parallels are equal to one another. 7. Show that the complements of the parallelograms which are about the diameter of any .parallelogram...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...•=• parts. Wherefore the opposite sides and angles, &c. PROP. XXXIV. THEOR. 3s. lEu. Parallelograms upon the same base, and between the same parallels, are equal to one another. PROP. XXXIV. FADE F \ . If the sides AD, DF, of the 1=1™ ABCD, DBCF, opp. to BC the base, be terminated...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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 ABC shall be equal...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - Liczba stron: 317
...adjacent angles of a parallelogram is equal to two right angles. PROP. XXXV. THEOR. Parallelograms upon, the same base and between the same parallels, are equal to one another. > (SEE THE 2d AND 3d FIGURES.) 34 If the sides AD, DF of the parallelograms ABCD, DBCF opposite to...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...two = parts. Wherefore the opposite sides and angles, &c. PROP. XXXIV. THEOR. 35. lEu. Parallelograms upon the same base, and be-tween the same parallels, are equal to one another. FA DEFAEDF \ . If the sides AD, DF, of the / — 7"" ABCD, DBCF, opp. to RC the base, be terminated...
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A course of practical geometry for mechanics

William Pease - 1846
...isosceles triangle required. The reason of this is (Prob. XXXVII. Bk. I. Euclid,) because triangles upon the same base, and between the same parallels, are equal to one another : ie the triangles ACB and AE B, being upon the base, AB, to which the line EC is parallel, therefore...
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A Complete Treatise on Practical Land-surveying: In All Its Departments ...

Anthony Nesbit - 1847 - Liczba stron: 426
...parallelogram ABCD, is equal to the parallelogram DBCE. (Euc. I. 35. Simp. II. 2. Em. HI. 6.) THEOREM VL Let the triangles ABC, DBC be upon the same base BC,...parallels AD, BC ; the triangle ABC is equal to the triangle DBC. (Euc. I. 37. Simp. II. 2. Em. II. 10.) THEOREM VH. Let ABC be a right-angled triangle,...
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