...BOB. The former of the above propositions seems to be a proper generalization of Euclid's theorem " that triangles on the same base and between the same parallels are equal." If we have any number of surfaces of definite extent, either plane or curved, and we form pyramids...

...which experience is equally incompetent to disprove or to confirm ? In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal," do we feel ourselves the less ready to give our assent to the demonstration, if it should be supposed,...

...which experience is equally incompetent to disprove or to confirm ? In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal," do we feel ourselves the less ready to give our assent to the demonstration, if it should be supposed,...

...sides equal to three given straight lines, of which any two whatever must be greater than the third. 5. Triangles on the same base and between the same parallels are equal to each other. 6. Describe a parallelogram which shall be equal to a given triangle, and have one of...

...equal to the parallelogram EFGH. [Axiom 1. Wherefore, parallelograms &c. QED PROPOSITION 87. THEOREM. Triangles on the same base, and between the same parallels, are equal. Let the triangles ABC, DBC be on the same base BC, and between the same parallels AD,BC: the triangle...

...between practical and theoretical knowledge, take proposition 37 in the first book of Euclid, shewing that triangles on the same base and between the same parallels are equivalent. The man with practical knowledge, is not only able to understand the demonstration, but...

...equal to the parallelogram EFGH. [Axiom 1. Wherefore, parallelograms &c. QED PROPOSITION 37. THEOREM. Triangles on the same base, and between the same parallels, are equal. Let the triangles ABC, DBC be on the same base BC, and between the same parallels AD,BC: the triangle...

...can expect to rear the fabric of scientific ethics. The perception or knowledge of any one that two triangles on the same base and between the same parallels are equal, is not the criterion of their equality. Their equality is a reality which does not depend upon the...

...Explain OBLONG, RHOMBOID, DIAGONAL. 7. Delineate a kite with mathematical accuracy. 8. Show by a drawing that triangles on the same base, and between the same parallels, are equal. 9. Why does not a bridge, when properly built, fall in f Make a drawing of such a bridge. 10. Distinguish...

...appears to mean that parallelograms on the same base and between the same parallels are equal, and also that triangles on the same base and between the same parallels are equal. See Geometry, Props. 35, 37.) * 6. Divide a6 - 3 aV + 3 aV - a? by a? - 3 a?x + 3 oo? -a?. (10.) as...