Elements of Geometry and Trigonometry |
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Page 41
... chord , or subtense of an arc , is the straight line FG , which joins its two extremities . † 4. A segment is the surface or portion of a circle , included between an arc and its chord . 5. A sector is the part of the circle included ...
... chord , or subtense of an arc , is the straight line FG , which joins its two extremities . † 4. A segment is the surface or portion of a circle , included between an arc and its chord . 5. A sector is the part of the circle included ...
Page 42
... AFB , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a circle . PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY .
... AFB , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a circle . PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY .
Page 43
PROPOSITION II . THEOREM . Every chord is less than the diameter . Let AD be any chord . Draw the radii CA , CD , to ... chords ; and , conversely , equal chords subtend equal arcs . Note . When reference is made from one proposition to ...
PROPOSITION II . THEOREM . Every chord is less than the diameter . Let AD be any chord . Draw the radii CA , CD , to ... chords ; and , conversely , equal chords subtend equal arcs . Note . When reference is made from one proposition to ...
Page 44
... chord EG , For , since the diameters AB , EF , are equal , the semi- circle AMDB may be applied M BE N exactly to ... chord AD is equal to the chord EG . Conversely , supposing again the radii AC , EO , to be equal , if the chord AD is ...
... chord EG , For , since the diameters AB , EF , are equal , the semi- circle AMDB may be applied M BE N exactly to ... chord AD is equal to the chord EG . Conversely , supposing again the radii AC , EO , to be equal , if the chord AD is ...
Page 45
... chord AD , of the first , is less than the chord AH of the second . PROPOSITION VI . THEOREM . The radius which is perpendicular to a chord , bisects the chord , and bisects also the subtended arc of the chord . Let AB be a chord , and ...
... chord AD , of the first , is less than the chord AH of the second . PROPOSITION VI . THEOREM . The radius which is perpendicular to a chord , bisects the chord , and bisects also the subtended arc of the chord . Let AB be a chord , and ...
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Common terms and phrases
adjacent altitude angle ACB ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 18 - If two triangles have two sides of the one equal to two sides of the...
Page 213 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 233 - It is, indeed, evident, that the negative characteristic will always be one greater than the number of ciphers between the decimal point and the first significant figure.
Page 287 - How many square feet are there in the convex surface of the frustum of a square pyramid, whose slant height is 10 feet, each side of the lower base 3 feet 4 inches, and each side of the upper base 2 feet 2 inches ? Ans.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.