 | Robert Gibson - Surveying - 1832 - 290 pages
...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.... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...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... | |
 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...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... | |
 | Euclides - 1834 - 518 pages
...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... | |
 | Francis Joseph Grund - Geometry, Plane - 1834 - 202 pages
...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.,... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...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... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...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... | |
 | Euclid - 1835 - 540 pages
...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... | |
 | Mathematics - 1835 - 684 pages
...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,... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...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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Parallelograms upon equal bases, and between the same parallels, are equal to one another. 
