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" Triangles upon equal bases, and between the same parallels, are equal to one another. "
The school Euclid: comprising the first four books, by A.K. Isbister - Side 43
av Euclides - 1862
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Logic, Deductive and Inductive

Thomas Fowler - 1895 - 365 sider
...which our deductive reasoning proceeds. The proposition proved in Euclid, Book i. Prop. 38, that ' Triangles upon equal bases, and between the same parallels, are equal to one another,' is derived from, or is the total result of, the previous deductions (i) that ' Parallelograms upon...
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Report of the Council of Public Instruction of the North-West Territories of ...

Northwest Territories Council of Public Instruction - 1897
...right angles. I. 32. Cor. 2. (6) Divide a right angle into five equal parts. 10. ('/) Parallelograms on equal bases and between the same parallels are equal to one another. I. 36. (6) Extend the proof of proposition (a) to any number of parallelograms. (c) Distinguish "equal...
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Mathematics: Mechanic's bids and estimates. Mensuration for beginners. Easy ...

Seymour Eaton - 1899 - 340 sider
...square shall be less than that of the parallelogram. Lesson No. 17 PROPOSITION 38. THEOREM Triangles on equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be on equal bases BC, EF, and between the same parallels BF, AD : then the...
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Report of the Department of Education for the Year ...

Manitoba. Department of Education - 1900
...so that ED is equal to twice BA. Prove that the angle DBC is equal to onethird of the angle ABC. 5. Triangles upon equal bases and between the same parallels are equal to one another. If E and D are the points of trisection (nearest to A) of the sides AB, AC of a triangle, and F the...
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Henley's Encyclopaedia of Practical Engineering and Allied Trades ...

1907
...form of an equation : 2DOA + 2DOC .-= 2DOB. Now the triangle DOA equals triangle BCO (for triangles on equal bases and between the same parallels are equal to one another— Euclid, 1.38). Therefore, 2DOA + 2DOC = 2BCO + 2DOC = 2DOB. Therefore the sum of the moments of P and...
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Henley's Encyclopædia of Practical Engineering and Allied Trades: A ...

Joseph Gregory Horner - 1907
...form of an equation : 2DOA + 2DOC - 2DOB. Now the triangle DOA equals triangle BCO (for triangles on equal bases and between the same parallels are equal to one another— Euclid, I. 38). Therefore, 2DOA + 2DOC = 2BCO + 2DOC = 2DOB. Therefore the sum of the moments of P...
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The Monist, Volum 19

Paul Carus - 1909
...of the article in a universal sense is regular in Greek. Euclid does not say "All parallelograms on equal bases and between the same parallels are equal to one another" but "the parallelograms" (TO. TOpoAAiyAoypo/t/aa) ; so in the famous 47th it is not "in all" but "In...
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The Sheet-Metal Worker's Instructor

R. H. Warn, John G. Horner - 2002 - 284 sider
...parallels, are equal to one another. (Euc. I. 37, and I. 38.) (jr) Parallelograms upon the same base, or upon equal bases, and between the same parallels, are equal to one another. (Enc. I. 35, and I. 36.) (7i) If a parallelogram and a triangle be upon the same base, and between...
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Euclid's Elements in Greek: Vol. I:

Richard Fitzpatrick - 2005 - 296 sider
...^apaXXr]Xoiç ïaa àXXrjXoiç èaiiv OTisp sSsi ELEMENTS BOOK l Proposition 38 В С EF Triangles which are on equal bases and between the same parallels are equal to one another. Let ABC and DEF be triangles on the equal bases BC and EF, and between the same parallels BF and AD....
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The popular educator, Volum 5

Popular educator - 1860
...angle at the base), the perpendicular will fall within the triangle, upon the base itself. PROPOSITION XXXVIII. THEOREM. Triangles upon equal bases, and...between the same parallels, are equal to one another. ng. 38. Inflg.38,letthetrianglesABC Ç AD н and D в F, be upon equal bases в о and EF, and .between...
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