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" Parallelograms upon equal bases, and between the same parallels, are equal to one another. "
The first three books of Euclid's Elements of geometry, with theorems and ... - Side 30
av Euclid, Thomas Tate - 1849 - 108 sider
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1832 - 290 sider
...parallelogram, AB will be = CD, and AD=BC. THEOREM XIII. PL. l.fig.3l 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 are parallel, then &e parallelogram ABDC—BDFE—EFHG....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 346 sider
...to the parallelogram EBCF. Therefore, parallelograms upon the same base, &c. QED PROP. XXXVI. THEOR. Parallelograms upon equal bases, and between the same...Join BE, CH; and because BC is equal to FG, and FG to (34. 1.) EH, BC is equal to EH ; and they -r> f 'K1 ff are parallels, and joined to- .\j Ja vr wards...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 168 sider
...triangles upon the same base, &c. Which was to be demonstrated. PROPOSITION XXXVIII. THEOREM. — Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon c ADH equal bases BC, EF, and between the same parallels AD, BF. The...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 sider
...Parallelograms upon equal bases, and between tht.'' same parallels, are equal to one another. 1) E H Let ABCD, EFGH be parallelograms upon equal bases...the same parallels AH, BG : the parallelogram ABCD shall be equal to EFGH. Join BE, CH : and because BC is equal t to KG, and FG to * EH, BC is equal...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Del 1

Francis Joseph Grund - 1834 - 202 sider
...4. The areas of all parallelograms, which have equal bases and heights, are equal to one another. 5. Parallelograms upon equal bases, and between the same parallels, are equal to one another. 6. The area of a parallelogram is found by multiplying the basis given in rods, feet, inches, &c.,...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 544 sider
...parallelograms upon the same base," &c. QED Book I. a 34. l. b 33. 1. c 35. 1. PROP. XXXVI. THEOR. Parallelograms upon equal bases, and between the same...BE, CH; and because BC is equal to FG, and FG to* EH, BC is equal to EH ; and they are parallels, and joined towards the same parts by the straight lines...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 336 sider
...PROP. XXX. THEOR. Parallelograms upon equal bases, and between the same parallels, are equivalent , to one another. Let ABCD, EFGH be parallelograms upon...equal bases BC, FG, and between the same parallels AH, . _ BG ; the parallelogram ABCD •«: JJ Jli H. is equal to EFGH. Join BE, CH ; and because BC is...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 sider
...equal to the triangle d 7. Ax. 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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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

1835 - 684 sider
...the same base and altitude. PROP. 27. (Eue. i. 37, 38, 39, & 40.) Triangles upon the same base, or upon equal bases, and between the same parallels, are equal to one another : and conversely, equal triangles, upon the same base, or upon equal bases in the same straight line,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 488 sider
...to the parallelogram EBCF. Therefore, parallelograms upon the same base, &c. QED PROP. XXXVI. THEOR. Parallelograms upon equal bases, and between the same...parallelograms upon equal bases BC, FG, and . between the same **• D , J,. parallels AH, BG ; the parallelogram ABCD is equal to EFGH. Join BE, CH; and because...
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