 | Euclides - 1864 - 448 pages
...the diameter BC divides 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 anuther. ( Let the parallelograms AB CD, -E-BCFbeuponthe same base 2? C, . and between the same... | |
 | Euclides - 1865 - 402 pages
...and the diameter BC divides the parallelogram ACI>B into two equal parts. QED PROP. XXXV.— THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to each other. (References— Prop. I 4, 29, 34 ; ax. 1, 3, 6.) Let the parallelograms ABCD, EBCF,... | |
 | Architecture - 1865 - 276 pages
...shall be equal. Given the vertical angle, and a side to construct the triangle. 3. Prop. 35. Theorem. Parallelograms upon the same base and between the same parallels are equal to one another. Shew this is equally true of triangles. 4. Prop. 44. — Problem. To a given straight... | |
 | William Harris Johnston - 1865 - 478 pages
...hold good as respects oblique parallelograms abo. By Euclid, Book I, Prop. 35, it is established that «parallelograms upon the same base and between the same parallels are equal to one another." Now, the perpendicular distance, D С, between the sides, DF and В С, of the oblique... | |
 | Euclides - 1865 - 80 pages
...the space ABCF, and the parallelogram ABCD is equal to the rectangle EBCF. PROPOSITION XLIV. 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 base BC, and between the same parallels... | |
 | J. F. H. de Rheims - Geometrical drawing - 1865 - 336 pages
...another, and the diameter bisects them, ie, divides them into two equal parts. Prop. 35. — Tfieorem. Parallelograms upon the same base and between the same parallels are equal to one another. Prop. 37. — Theorem. Triangles upon the same base and between the same parallels... | |
 | E. M. Reynolds - Geometry - 1868 - 172 pages
...triangle HKD= the triangle GDK; Therefore the remaining figure AK= the remaining figure KC. THEOREM II. Parallelograms upon the same base and between the same parallels are equal. itetABCD, EBCF be parallelograms upon the same base BC and between the same parallels BC and AF, they... | |
 | Thomas Squire Barrett - Causation - 1871 - 252 pages
...but be ' true ; as that 1 9 and 1 1 are 30 ; — Exam, of Antitheos, part i. §§ 64 — 65. ' that parallelograms upon the same ' base and between the same parallels ' are equal ; — that all the angles in ' the same segment of a circle are ' equal. The latter are truths which... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...and EDF be equal angles then the areas of the sectors BAC and EDF will be also equal. PROPOSITION 4. Parallelograms upon the same base and between the same parallels are equal to one another in area. Fig, n. Fig. 12. C ED.FCDEP Let the two parallelograms CABD and EABF be upon... | |
 | Thomas Squire Barrett - Causation - 1872 - 254 pages
...former kind ' are truths which cannot but be ' true ; as that 1 9 and 1 1 are 30 ; — NOTE XIX. that parallelograms upon the same base and between the same parallels are equal ; — that all the angles in the same segment of a circle are equal. The latter are truths which it... | |
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Parallelograms upon the same base and between the same parallels, are equal to one another. 
