Plane GeometrySilver, Burdett, 1896 - 253 Seiten |
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Seite 87
... touch each other and also the outer circumference . that the perimeter ABC equals the diameter of the outer circle . 152. ABC is a triangle inscribed in a circle whose centre is O , and OD is drawn perpendicular to AC . Prove that ZAOD ...
... touch each other and also the outer circumference . that the perimeter ABC equals the diameter of the outer circle . 152. ABC is a triangle inscribed in a circle whose centre is O , and OD is drawn perpendicular to AC . Prove that ZAOD ...
Seite 88
... touch two indefinite lines which are perpendicular to each other . What is the locus of the middle point of the moving line ? 166. What is the locus of the vertex of the right angle of a right tri- angle which has a given hypotenuse ...
... touch two indefinite lines which are perpendicular to each other . What is the locus of the middle point of the moving line ? 166. What is the locus of the vertex of the right angle of a right tri- angle which has a given hypotenuse ...
Seite 112
... distant O described about O as a centre , with radius OF ( 1 to ED ) , will be an inscribed O chords of outer [ ob , by hyp er ] = will touch sides of Lpolygon f ] 227. Definitions . The radius of a regular polygon is 112 PLANE GEOMETRY.
... distant O described about O as a centre , with radius OF ( 1 to ED ) , will be an inscribed O chords of outer [ ob , by hyp er ] = will touch sides of Lpolygon f ] 227. Definitions . The radius of a regular polygon is 112 PLANE GEOMETRY.
Seite 119
... touch each other , straight lines drawn through the point of tangency are cut proportionally by the circumferences . 215. Two secants are drawn to a circle from an outside point and their external segments are 20 and 24. If the internal ...
... touch each other , straight lines drawn through the point of tangency are cut proportionally by the circumferences . 215. Two secants are drawn to a circle from an outside point and their external segments are 20 and 24. If the internal ...
Seite 166
... touch two perpendiculars . In what position is AB when the triangle formed by the two lines is a maximum ? If AB = 10 , what is that area ? PROPOSITION XXX 297. Theorem . Of isoperimetric polygons of the 166 PLANE GEOMETRY.
... touch two perpendiculars . In what position is AB when the triangle formed by the two lines is a maximum ? If AB = 10 , what is that area ? PROPOSITION XXX 297. Theorem . Of isoperimetric polygons of the 166 PLANE GEOMETRY.
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Häufige Begriffe und Wortgruppen
AB² ABCD AC² acute angle AD² adjacent angles altitude angles are equal apothem Appl base and altitude base angle BC² BD² bisector bisects central angle centre chord circumf circumference circumscribed circle Cons decagon diagonals diameter dist distance divided Draw equal circles equally distant equiangular equiangular polygon equilateral triangle EXERCISES exterior angle feet figure Find its area Find the area geometric given circle given line given point homologous sides hypotenuse intersecting isosceles trapezoid isosceles triangle length locus logarithm mantissa mean proportional meas measure median middle point number of sides parallel parallelogram perimeter perpendicular Problem produced PROPOSITION quadrilateral radii radius ratio rectangle regular hexagon regular inscribed regular polygon respectively rhombus right angle right triangle secant segments similar triangles subtended tang tangent Theorem third side trapezoid triangle ABC triangles are equal vertex vertical angle
Beliebte Passagen
Seite 60 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Seite 219 - ... 4. Prove that, if from a point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and the part without the circle.
Seite 139 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Seite 44 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Seite 43 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 217 - Show that the areas of similar triangles are to each other as the squares of the homologous sides.
Seite 89 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Seite 107 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Seite 218 - 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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove = — • A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Seite 218 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.