An Elementary Treatise on Geometry: Simplified for Beginners Not Versed in Algebra. Part I, Containing Plane Geometry, with Its Application to the Solution of Problems, Part 1 |
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Page 23
... side of the line AC . ( See Truth VII . ) D Q. Can you prove the same of the ... side of the straight line AC , taking again a right angle for the measure ? A A. It is also equal to two right angles . Q. Why ? -C A ... AB , CD GEOMETRY . 23.
... side of the line AC . ( See Truth VII . ) D Q. Can you prove the same of the ... side of the straight line AC , taking again a right angle for the measure ? A A. It is also equal to two right angles . Q. Why ? -C A ... AB , CD GEOMETRY . 23.
Page 25
... side ab to its equal AB , the side ac will fall upon AC , and bc upon BC ; because the angles at a and A , b and B , are respectively equal ; and as the sides ac , bc , take the same direction as the sides AC , BC , they must also meet ...
... side ab to its equal AB , the side ac will fall upon AC , and bc upon BC ; because the angles at a and A , b and B , are respectively equal ; and as the sides ac , bc , take the same direction as the sides AC , BC , they must also meet ...
Page 26
... sides of the line GH . Now if the lines AB , CD , are not parallel , they must either be converging or diverging . If they are converging , AB and CD will , when sufficiently extended , cut each other somewhere , say in M ; but then ...
... sides of the line GH . Now if the lines AB , CD , are not parallel , they must either be converging or diverging . If they are converging , AB and CD will , when sufficiently extended , cut each other somewhere , say in M ; but then ...
Page 27
... AB , and afterwards extended until , in the point R , it strikes the line CD . A. I should first observe that the triangles OPF and ORI are equal ; because the triangle OPF has a side and two adjacent angles equal to a side and two ...
... AB , and afterwards extended until , in the point R , it strikes the line CD . A. I should first observe that the triangles OPF and ORI are equal ; because the triangle OPF has a side and two adjacent angles equal to a side and two ...
Page 28
... sides ( remarks to Query 6 , page 25 ) ; conse- quently the two lines AB , CD , are both perpendicular to the same straight line PR , and therefore parallel to each other . ( Last query . ) A E H Q. Supposing , now , two straight lines , AB ...
... sides ( remarks to Query 6 , page 25 ) ; conse- quently the two lines AB , CD , are both perpendicular to the same straight line PR , and therefore parallel to each other . ( Last query . ) A E H Q. Supposing , now , two straight lines , AB ...
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Common terms and phrases
adjacent angles angle ABC angle ACB angle x basis bisected called centre chord circle whose radius circum circumference consequently degrees DEMON diagonal diameter dividing the product draw the lines equal angles equal sides equal triangles exterior angle feet figure ABCDEF found by multiplying fourth term geometrical proportion given angle given circle given triangle gles height hypothenuse inches isosceles triangle JOHN FARRAR length let fall line AB line AC line CD line MN mean proportional measures half number of sides parallel lines parallelogram ABCD perpendicular Plane Geometry points of division PROBLEM prove quadrilateral radii radius rectangle rectilinear figure regular inscribed regular polygon ABCDEF Remark rhombus right angles right-angled triangle second term Sect semicircle side AB side AC similar triangles smaller SOLUTION subtended tangent third line third term three angles three sides trapezoid triangle ABC triangles are equal Truth vertex
Popular passages
Page 144 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 68 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...
Page 124 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 111 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 106 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Page 117 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems.
Page 144 - A, with a radius equal to the sum of the radii of the given circles, describe a circle.
Page 80 - ... any two triangles are to each other as the products of their bases by their altitudes.
Page 125 - P is at the center of the circle. II. 18. The sum of the arcs subtending the vertical angles made by any two chords that intersect, is the same, as long as the angle of intersection is the same. 19. From a point without a circle two straight lines are drawn cutting the convex and concave circumferences, and also respectively parallel to two radii of the circle. Prove that the difference of the concave and convex arcs intercepted by the cutting lines, is equal to twice the arc intercepted by the radii.