...= E, and C = F, we may thence infer that the other three are also equal, namely, *4fi = DE, AC — DF, and A = D. THEOREM. 40. One side of a triangle...two. Fig. 23. Demonstration. The straight line BC (Jig. 23), for example* is the shortest way from B to C (3) ; BC therefore is less than BA+AC. THEOREM....

...C = F, we may thence infer that the other three are also equal, namely, AB = DE, AC=DF, and .#=£>. THEOREM. 40. One side of a triangle is less than the...C (3) ; BC therefore is less than BA+AC. THEOREM. Fig.84. 41. Jf from a point O (fig. 24), vilhin a triangle ABC, there be drawn straight lines OB, OC,...

...the other three are also equal, namely, AB = DE, THEOREM. 9 40. One side of a triangle is less titan the sum of the other two. Fig. 23. Demonstration....shortest way from -B to C (3) ; BC therefore is less than BA + AC. THEOREM. Fig. 24. 41. If from a point O (fig. 24), within a triangle ABC, there be drawn straight...

...E, and C = F, we may thence infer that the other three are also equal, namely, AB = DE, THEOREM. f % 40. One side of a triangle is less than the sum of...two. Fig. 23. Demonstration. The straight line BC (Jig. 23), for example, is the shortest way from B to C (3) ; BC therefore is less than BA+AC. THEOREM....

...each of the triangles BEF, CEF, GEF, a radius, and the side EF common, which are equal to AF : but one side of a triangle is less than the sum of the other two (a) ; therefore FG, FC, or FB is less than FA, which passes through the centre. 2. And, because EG,...

...proved, and problems, operations to be performed. The following are examples of propositions : Any one side of a triangle is less than the sum of the other two ; a diameter divides a circle and its circumference into two equal parts. The following are examples...

...or arcs, are equal. 13. A straight line is the shortest distance between two points. Corollary. — One side of a triangle is less than the sum of the other two. 14. But one straight line can be drawn between two points.* EXERCISE WITH RULE AND DIVIDERS UPON THE-...

...aADCswaACD? 73.1. ADC tx, BCD? .-. In*DBC, BCswBD? 73. But, as AD = AC, BD xx BA + AC ? § 78. THEOR. X. Any side of a triangle is less than the sum of the other two. [Proved by the aid of Theor. IXl COR. I. The difference between any two sides of a triangle is less...

...of truth, represented by the Conception, and not by any means or necessarily of any diagram * " Any one side of a triangle is less than the sum of the two other sides." which we may draw, or of any piece of matter which may be brought into the form of...

...of truth, represented by the Conception, and not by any means or necessarily of any diagram ? " Any one side of a triangle is less than the sum of the two other sides." which we may draw, or of any piece of matter which may be brought into the form of...