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TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Inventional Geometry: A Series of Problems, Intended to Familiarize the ... - Página 43
por William George Spencer - 1877 - 97 páginas
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

...College. WILLIAM HENRY BESAHT, MA St John's College. TUESDAY, January 6, 1857. 9... 12. 1. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. ABC is an isosceles triangle, of which A is the vertex : AB, AC, are bisected in D and E respectively...
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A course of practical geometry for mechanics

William Pease - 1856
...to meet these perpendiculars, and the required rectangle will be formed. REASON : " Parallelograms, upon the same base, and between the same parallels," are equal to each other. (Euclid, Book I. Prop. 35.) PROBLEM LXX. To make a rectangle, one of its sides being given,...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...extensive use in the construction and measurement of Geometrical Figures. \ TO \ i / PROP. 37. — THEOR. Triangles upon the same base and between the same parallels are equal to one another. CONSTRUCTION. — Pst. 2. A st. line may be produced in a st. line. P. 31. Through a given point to...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 12 páginas
...If the words printed above in italics be omitted, would the proposition as then stated be true ? 2. Triangles upon the same base, and between the same parallels, are equal to one another. Divide a given triangle into four equal parts. 3. "What is a rectangle ? If a straight line be divided...
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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volumen1

Euclides - 1868
...HC 4 P. 33. 5 Def. A. 6 D. 5. H. 7 P. 35. 8 P. 85. 9 Ax. 1. 10 Becap. • PilOP. XXXVII. Тикоа. Triangles upon the same base and between the same parallels are equal to one ano CON. Pst. 2. P. 31. Def. A. DEM. P. 35. 34. Ax. 7. SCHOL. PIIOP. XXXVIII. TIIEOU. Triangles upon...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 páginas
...shall be greater than the base of the other. 2. Define a parallelogram ; prove that parallelograms 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 of the whole line and of one of the...
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The examination papers as set for the preliminary literary examination of ...

...triangle are greater than the third. Show that the difference of any two sides is less than the third. 5. Triangles upon the same base and between the same parallels are equal to one another. 6. If the square described upon one of the sides of a triangle be equal to the squares described upon...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...parallelogram EBCH ; therefore (Ax. 1) the parallelogram ABCD is equal to EFGH. PROPOSITION XXXVII. THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. Given the triangles ABC and DEC upon the same base BC, and between the same parallels AD and BC ; to...
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Cambridge senate-house problems and riders for the year 1860; with solutions ...

Henry William Watson - 1860
...rectangle contained by AB and CD, the rect. AB, CD. 1. DEFINE parallel straight lines. Parallelograms upon the same base, and between the same parallels, are equal to one another. If a straight line DME be drawn through the middle point M of the base BC of a triangle ABC, so as...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 páginas
...-BCdivides the parallelogram A CDB 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 AB CD, EBCF be upon the same base 2? C, and between the same parallels AF, BC....
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