Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is Added a Book on Proportion, with Notes and Illustrations |
From inside the book
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Page 16
... triangle , which has an obtuse an- Δ Δ Δ The right - angled triangle , which has a right - angle . The side opposite the right - angle is called the hypothenuse . Thus , the tri- angle ABC is right - angled at A ; and B the side BC is ...
... triangle , which has an obtuse an- Δ Δ Δ The right - angled triangle , which has a right - angle . The side opposite the right - angle is called the hypothenuse . Thus , the tri- angle ABC is right - angled at A ; and B the side BC is ...
Page 24
... triangle DEF coincides with the triangle ABC throughout , consequently they are equal . ( Ax . 13. ) Hence , universally , Any two triangles are every way equal , when two sides and the included angle of the one , are respectively equal ...
... triangle DEF coincides with the triangle ABC throughout , consequently they are equal . ( Ax . 13. ) Hence , universally , Any two triangles are every way equal , when two sides and the included angle of the one , are respectively equal ...
Page 25
... triangle , any side is less than the sum of the other two . For the straight line BC , for example , is the shortest distance from B to C ; ( Def . 5 ; ) therefore , BC is less than BA + AC . Hence , In every triangle , & c . A B C ...
... triangle , any side is less than the sum of the other two . For the straight line BC , for example , is the shortest distance from B to C ; ( Def . 5 ; ) therefore , BC is less than BA + AC . Hence , In every triangle , & c . A B C ...
Page 26
... triangle . PROPOSITION IX . THEOREM . If the two sides AB , AC , of the triangle ABC , are respective- ly equal to the two sides DE , DF , of the triangle DEF , while , at the same time , the angle BAC contained by the for- mer , is ...
... triangle . PROPOSITION IX . THEOREM . If the two sides AB , AC , of the triangle ABC , are respective- ly equal to the two sides DE , DF , of the triangle DEF , while , at the same time , the angle BAC contained by the for- mer , is ...
Page 27
... triangle ABC are respectively equal to the two DE , DF of the triangle DEF , while the third side , CB of the first tri- angle , is greater than the third EF of the second ; then will the angle BAC of the first triangle be greater than ...
... triangle ABC are respectively equal to the two DE , DF of the triangle DEF , while the third side , CB of the first tri- angle , is greater than the third EF of the second ; then will the angle BAC of the first triangle be greater than ...
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...
Bibliographic information
| Title | Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is Added a Book on Proportion, with Notes and Illustrations Day and Thomson's Elementary course of mathematics for schools and academies |
| Author | James Bates Thomson |
| Edition | 3 |
| Publisher | Durrie and Peck, 1844 |
| Original from | the New York Public Library |
| Digitized | 21 Jun 2006 |
| Length | 237 pages |
| Export Citation | BiBTeX EndNote RefMan |