# Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is Added a Book on Proportion, with Notes and Illustrations

Durrie and Peck, 1844 - 237 σεκΏδερ

### ‘ι κίμε οι ςώόστερ -”ΐμτανγ ξώιτιξόρ

Ρεμ εμτοπΏσαλε ξώιτιξίρ στιρ σθμόηειρ τοποηεσΏερ.

### –εώιεςϋλεμα

 ≈μϋτγτα 1 1 ≈μϋτγτα 2 3 ≈μϋτγτα 3 5 ≈μϋτγτα 4 12 ≈μϋτγτα 5 12 ≈μϋτγτα 6 12 ≈μϋτγτα 7 12 ≈μϋτγτα 8 12
 ≈μϋτγτα 14 57 ≈μϋτγτα 15 63 ≈μϋτγτα 16 72 ≈μϋτγτα 17 73 ≈μϋτγτα 18 79 ≈μϋτγτα 19 86 ≈μϋτγτα 20 88 ≈μϋτγτα 21 92

 ≈μϋτγτα 9 12 ≈μϋτγτα 10 13 ≈μϋτγτα 11 16 ≈μϋτγτα 12 29 ≈μϋτγτα 13 48
 ≈μϋτγτα 22 132 ≈μϋτγτα 23 147 ≈μϋτγτα 24 166 ≈μϋτγτα 25 169 ≈μϋτγτα 26 221

### Ργλοωικό αποσπήσλατα

”εκΏδα 196 - THEOREM. Every section of a sphere, made by a plane, is a circle.
”εκΏδα 176 - AT into equal parts .Ax, xy, yz, &c., each less than Aa, and let k be one of those parts : through the points of division pass planes parallel to the plane of the bases : the corresponding sections formed by these planes in the two pyramids will be respectively equivalent, namely, DEF to def, GHI to ghi, &c.
”εκΏδα 125 - AB as a diameter, describe a semicircle : at the extremity of the diameter draw the tangent AD, equal to the side of the square C ; through the point D and the centre O draw the secant DF ; then will DE and DF be the adjacent sides of the rectangle required. For...
”εκΏδα 229 - The area of the circle, we infer therefore, is equal to 3.1415926. Some doubt may exist perhaps about the last decimal figure, owing to errors proceeding from the parts omitted ; but the calculation has been carried on with an additional figure, that the final result here given might be absolutely correct even to the last decimal place. Since the...
”εκΏδα 118 - B, may be found in the same manner, for it will be the same as a fourth proportional to the three lines A, B, B. PROBLEM IIL To find a mean proportional between two given lines A and B.
”εκΏδα 176 - DEF, def, are equivalent; for like reasons, the third exterior prism GHI-K and the second interior prism ghi-d are equivalent; the fourth exterior and the third interior ; and so on, to the last in each series. Hence all the exterior prisms of the pyramid...
”εκΏδα 46 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
”εκΏδα 220 - Let it be granted that a straight line may be drawn from any one point to any other point.
”εκΏδα 101 - In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle.
”εκΏδα 227 - The surface of a regular inscribed polygon, and that of a similar polygon circumscribed, being given ; to find the surfaces of the regular inscribed and circumscribed polygons having double the number of sides. Let AB be a side of the given inscribed polygon ; EF, parallel to AB, a side of the circumscribed polygon ; C the centre of the circle. If the chord AM and the tangents AP, BQ, be drawn, AM...