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 119
... describing from the point O , as a centre , with a radius OA , a circle around the polygon ABCDEF , each of the vertices A , B , C , D , E , F , will be in the cir- cumference of the circle . Q. What other important consequence follows ...
... describing from the point O , as a centre , with a radius OA , a circle around the polygon ABCDEF , each of the vertices A , B , C , D , E , F , will be in the cir- cumference of the circle . Q. What other important consequence follows ...
Page 120
... describe with a radius Og the circumfer- ence of a circle , that circumference will touch the middle of the sides AB ... describing a circle around each of the regular polygons abcdef , ABCDEF , and drawing the radii Oa , Ob , Oc , Od ...
... describe with a radius Og the circumfer- ence of a circle , that circumference will touch the middle of the sides AB ... describing a circle around each of the regular polygons abcdef , ABCDEF , and drawing the radii Oa , Ob , Oc , Od ...
Page 141
... describe an arc of a circle , and from the point B , with the A same radius , AB , another arc cutting the first . B 2. From the point of intersection , C , draw the lines AC , BC ; the triangle ABC will be equilateral . DEMONSTRATION ...
... describe an arc of a circle , and from the point B , with the A same radius , AB , another arc cutting the first . B 2. From the point of intersection , C , draw the lines AC , BC ; the triangle ABC will be equilateral . DEMONSTRATION ...
Page 142
... describe an arc of a circle , and from the point A , with the same radius , another arc , cutting the first . 3. Through the point of intersection , C , and the point D , draw a straight line , CD , which will be perpendicular to the ...
... describe an arc of a circle , and from the point A , with the same radius , another arc , cutting the first . 3. Through the point of intersection , C , and the point D , draw a straight line , CD , which will be perpendicular to the ...
Page 143
... describe the circumference of a circle . 2. Through the point B and the centre O , of the cir- cle , draw the ... describe an arc of a circle ; and from the two points D and E , where this arc cuts the legs of the given angle , with the ...
... describe the circumference of a circle . 2. Through the point B and the centre O , of the cir- cle , draw the ... describe an arc of a circle ; and from the two points D and E , where this arc cuts the legs of the given angle , with the ...
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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 circumscribed circles 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 straight line given triangle gles height hypothenuse inches isosceles triangle length let fall line AB line AC line CD line MN mean proportional measures half number of sides parallel lines parallelogram ABCD perpendicular points of division PROBLEM prove quadrilateral radii radius rectangle rectilinear figure 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 2 - District Clerk's Office. BE IT REMEMBERED, that on the tenth day of August, AD 1829, in the fifty-fourth year of the Independence of the United States of America, JP Dabney, of the said district, has deposited in this office the title of a book, the right whereof he claims as author, in the words following, to wit...
Page 78 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...
Page 2 - CLERK'S OFFIcE. BE it remembered, that on the eleventh day of November, AD 1830, in the fiftyfifth year of the Independence of the United States of America, Gray & Bowen, of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit...
Page 136 - 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 121 - 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 137 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Page 127 - 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 154 - A, with a radius equal to the sum of the radii of the given circles, describe a circle.
Page 90 - ... any two triangles are to each other as the products of their bases by their altitudes.
Page 137 - 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.