Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is Added a Book on Proportion, with Notes and Illustrations |
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Page 12
... Diameter , Chords , Areas , & c . , 50-57 The Measurement of Angles , & c . , 58-62 Problems relating to the First two Books , 63-72 Ratio and Proportion , BOOK III . BOOK IV . The Measurement of Surfaces and the Proportion of Figures ...
... Diameter , Chords , Areas , & c . , 50-57 The Measurement of Angles , & c . , 58-62 Problems relating to the First two Books , 63-72 Ratio and Proportion , BOOK III . BOOK IV . The Measurement of Surfaces and the Proportion of Figures ...
Page 48
... diameter . From the definition of a circle , it follows that all the radii are equal ; also , that all the diameters are equal , and each is double of the radius . 3. A portion of the circumference , such as FHG , is called an arc . The ...
... diameter . From the definition of a circle , it follows that all the radii are equal ; also , that all the diameters are equal , and each is double of the radius . 3. A portion of the circumference , such as FHG , is called an arc . The ...
Page 49
... sides are tangents to the circumference . ( See the diagram of Prop . 7. 5. ) In the same case , the circle is said to be in- scribed in the polygon . 5 PROPOSITION I. THEOREM . The diameter AB , divides the BOOK II . 49.
... sides are tangents to the circumference . ( See the diagram of Prop . 7. 5. ) In the same case , the circle is said to be in- scribed in the polygon . 5 PROPOSITION I. THEOREM . The diameter AB , divides the BOOK II . 49.
Page 50
... diameter AB , divides the circle AFB and its circumfer- ence into two equal parts . For , if the figure AEB be ... diameter bisects the circle and its circumference . B PROPOSITION II . THEOREM . The chord AD , is less than the diameter ...
... diameter AB , divides the circle AFB and its circumfer- ence into two equal parts . For , if the figure AEB be ... diameter bisects the circle and its circumference . B PROPOSITION II . THEOREM . The chord AD , is less than the diameter ...
Page 51
... diameters AB , EF are equal , the semicircle AMDB may be applied exactly to the semicircle ENGF , and the curve line AMDB will coincide entirely with the curve line ENGF . But the part AMD is equal to the part ENG by hypothesis , hence ...
... diameters AB , EF are equal , the semicircle AMDB may be applied exactly to the semicircle ENGF , and the curve line AMDB will coincide entirely with the curve line ENGF . But the part AMD is equal to the part ENG by hypothesis , hence ...
Common terms and phrases
Abridgment of Day's adjacent angles allel altitude angle ACB angle BAC antecedent base ABCD bisect centre chord circ circle circumference circumscribed polygon common cone consequently convex surface couplets cylinder Day's Algebra diagonal diameter divided draw drawn equal and parallel equal angles equally distant equiangular equilateral triangles equivalent four magnitudes frustum geometry greater half homologous sides hypothenuse hypothesis inscribed polygon interior angles intersection let fall manner mean proportional measured number of sides oblique lines opposite parallelogram pendicular perimeter perpendicular plane angles plane MN polyedron polygon ABCDE President Day prism PROBLEM Prop PROPOSITION XI pyramid SABCDE quadrilateral quantity radii radius ratio rectangle regular polygon respectively equal SABC Scholium Schools and Academies segment similar solid angle sphere square described straight line tangent THEOREM Thomson trapezium triangle ABC triangular prism vertex Yale College
Popular passages
Page 196 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Page 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.
Page 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...
Page 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...
Page 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.
Page 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...
Page 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.
Page 220 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 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.
Page 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...