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" Triangles upon equal bases, and between the same parallels, are equal to one another. "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Σελίδα 26
των Dennis M'Curdy - 1846 - 138 σελίδες
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Solutions of the Problems and Riders Proposed in the Senate-house ...

William Walton - 1864 - 212 σελίδες
...AB is "sq. on AB," and for the rectangle contained by AB and CD, " the rect. AB, CD." l. TKIANGLES upon equal bases and between the same parallels are equal to one another. If a quadrilateral figure have two sides parallel, and the parallel sides be bisected, the line joining...

The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...Parallelograms upon the same base, and between the same paral' k-ls. are equal to one another. Prop. 36. Parallelograms upon equal bases, and between the same parallels, are equal to one another. Prop. 37. Triangles upon the same base, and between the same parallels, are equal to one another. Prop....

Elements of plane geometry, book i, containing nearly the same propositions ...

Euclides - 1865
...EBCH; therefore the parallelogram ABCD is likewise equal to the parallelogram EFGH. Cor. Triangles upon equal bases and between the same parallels are equal to one another. For the diagonals AC, EG bisect the parallelograms, and therefore (Ax. 7) the triangle ABC is equal...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 σελίδες
...EBCF. Wherefore, parallelograms on the same base &c. QBD PROPOSITION 36. THEOREM. Parallelograms on equal bases, and between the same parallels, are equal to one another. Let ABCD, EFGH be parallelograms on equal bases BC, FG, and between the same parallels AH, BG : the parallelogram ABCD...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 σελίδες
...ABC is equal to the triangle DBG. Wherefore, triangles &c. QED 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 : the triangle...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 σελίδες
...the parallelogram-KBCR Therefore, parallelograms upon the same, &c. QED PROPOSITION XXXVI. THEOREM. Parallelograms upon equal bases and between the same parallels, are equal to one another. Let ABCD, EFGHbe parallelograms upon equal bases BC, FG, and between the same parallels AH, BG. ADEH Join BE,...

The New York Teacher, and the American Educational Monthly, Τόμος 5

1868
...at this, if it is your case. See if you can make an affidavit, of your own knowledge, that triangles upon equal bases and between the same parallels are equal to one another, and that any two sides of a triangle are together greater than the third side ; and so on with all...

Parliamentary Papers, Τόμος 21

Great Britain. Parliament. House of Commons - 1869
...deducting fire-place of 4 feet 4 inches, and two windows, each 6 feet by 3 feet 2 inches. 3. Prove that parallelograms upon equal bases and between the same parallels are equal to one another. 4. It is required to describe a square equal to a given rectilineal figure. 5. The squares of the diagonals...

Minutes of the General Council of Medical Education & Registration ..., Τόμος 6

General Medical Council (Great Britain) - 1869
...is 1800Z.: what is the amount of the bill? EUCLID AND ALGEBRA. 1. Bisect a given straight line. 2. Parallelograms upon equal bases and between the same parallels are equal to one another. 3. The angle at the centre of a circle is double of the angle at the circumference upon the same base....

The elements of inductive logic

Thomas Fowler - 1870 - 348 σελίδες
...equal to one another,' is derived from, or is the total result of, the previous deductions (i) that ' Parallelograms upon equal bases, and between the same parallels, are equal to one another,' (2) that 'Triangles formed by the diagonal of a parallelogram are each of them equal to half the parallelogram'...




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