Books Books Parallelograms upon the same base and between the same parallels, are equal to one another. Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Page 111
by Thomas Perronet Thompson - 1833 - 150 pages ## Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 1

Euclides - 1868 - 88 pages
...HC 4 P. 33. 5 Def. A. 6 D. 5. H. 7 P. 35. 8 P. 85. 9 Ax. 1. 10 Becap. • PilOP. XXXVII. Тикоа. Triangles upon the same base and between the same parallels are equal to one ano CON. Pst. 2. P. 31. Def. A. DEM. P. 35. 34. Ax. 7. SCHOL. PIIOP. XXXVIII. TIIEOU. Triangles upon... ## Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 672 pages
...shall be greater than the base of the other. 2. Define a parallelogram ; prove that parallelograms upon the same base and between the same parallels are equal to one another. 3. If a straight line be divided into any two parts, the squares of the whole line and of one of the... ## Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...is equal to the same parallelogram EBCH ; therefore (Ax. 1) the parallelogram ABCD is equal to EFGH. PROPOSITION XXXVII. THEOREM. Triangles upon the same...between the same parallels, are equal to one another. Given the triangles ABC and DEC upon the same base BC, and between the same parallels AD and BC ; to... ## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...-BCdivides 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 another. Let the parallelograms AB CD, EBCF be upon the same base 2? C, and between the same parallels AF, BC. Then... ## The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860 - 336 pages
...triangle are greater than the third. Show that the difference of any two sides is less than the third. 5. Triangles upon the same base and between the same parallels are equal to one another. 6. If the square described upon one of the sides of a triangle be equal to the squares described upon... ## Cambridge Senate-house Problems and Riders for the Year 1860: With Solutions

Henry William Watson, Edward John Routh - Mathematics - 1860 - 240 pages
...rectangle contained by AB and CD, the rect. AB, CD. 1. DEFINE parallel straight lines. Parallelograms upon the same base, and between the same parallels, are equal to one another. If a straight line DME be drawn through the middle point M of the base BC of a triangle ABC, so as... ## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1860 - 332 pages
...same EBCH : Therefore also the parallelogram ABOI? it «qual to EFGH. PROP. XXXVII. THEOR. Trim gles upon the same base, and between the same parallels, are equal to ont another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels, AD,... ## Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 pages
...less than — — . MATHEMATICS. REV. CANON HEAVISIDE, MA Voluntary Paper, No. II. 1. Parallelograms upon the same base and between the same parallels are equal to one another. 2. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained... ## Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 pages
...parallelogram EFGH. (ax. 1.) Conclusion. — Therefore, parallelograms, &c. QED PROPOSITION 37.— THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. (References— Prop. I. 31, 34, 35; ax. 7.) Hypothesis. — Let the triangles ABC, DBC, be on the same... 