 | 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 - 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 - 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... | |
 | Henry William Watson - 1871 - 320 pages
...BAC 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 - 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... | |
 | Thomas Squire Barrett - 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... | |
 | Euclid, Charles Peter Mason - 1872 - 216 pages
...a parallelogram is divided into two equal parts by either of its diagonals. (Prop. XXXIV.) 2. That parallelograms upon the same base and between the same parallels are equal. (Prop. XXXV.) 3. That the halves of equals are equal. (Ax. VIII.) Let ABC and ABD be two As upon the... | |
 | Philip Kelland - 1873 - 248 pages
...to the sum of the squares of the sides. Retaining the notation and figure of Ex. 1, Art. 7, DA=a-ß; and, changing all the signs, we get (20) for the corresponding...angle. Adopting the figure of Euclid I. 35 and writing TVßа as the tensor multiplier of Vßa so as to drop the vector e on both sides ; we have, calling... | |
 | Edward Atkins - 1874 - 426 pages
...parallelogram ABCD into two equal parts. Therefore, the opposite sides, <fec. QED Proposition 35. — Theorem. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms A BCD, EBCF be on the same base BC, and between the same parallels... | |
 | Euclides - 1874 - 342 pages
...diameter BC divides the parallelogram ACDB into two equal parts. ~ QED PROPOSITION 35. — 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... | |
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Parallelograms upon the same base and between the same parallels, are equal to one another. 
