| William Pease - 1856
...to meet these perpendiculars, and the required rectangle will be formed. REASON : " Parallelograms, **upon the same base, and between the same parallels," are equal to** each other. (Euclid, Book I. Prop. 35.) PROBLEM LXX. To make a rectangle, one of its sides being given,... | |
| Euclides - 1858
...extensive use in the construction and measurement of Geometrical Figures. \ TO \ i / PROP. 37. — **THEOR. Triangles upon the same base and between the same parallels are equal to one another.** CONSTRUCTION. — Pst. 2. A st. line may be produced in a st. line. P. 31. Through a given point to... | |
| War office - 1858 - 12 Seiten
...If the words printed above in italics be omitted, would the proposition as then stated be true ? 2. **Triangles upon the same base, and between the same parallels, are equal to one another.** Divide a given triangle into four equal parts. 3. "What is a rectangle ? If a straight line be divided... | |
| Euclides - 1868
...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... | |
| Sandhurst roy. military coll - 1859 - 1869 Seiten
...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... | |
| Robert Potts - 1860 - 361 Seiten
...-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... | |
| Euclides - 1860
...parallelogram EBCH ; therefore (Ax. 1) the parallelogram ABCD is equal to EFGH. PROPOSITION XXXVII. THEOREM. **Triangles upon the same base, and 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... | |
| Royal college of surgeons of England - 1860
...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... | |
| Henry William Watson - 1860
...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... | |
| John Playfair - 1860 - 317 Seiten
...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,... | |
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