The Essentials of GeometryD.C. Heath & Company, 1899 - 395 σελίδες |
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Σελίδα 122
... proportional between the first and last terms , and the last term is called a third proportional to the first and second terms . Thus , in the proportion a : bb : c , b is a mean propor- tional between a and c , and c a third ...
... proportional between the first and last terms , and the last term is called a third proportional to the first and second terms . Thus , in the proportion a : bb : c , b is a mean propor- tional between a and c , and c a third ...
Σελίδα 123
... proportional between two quantities is equal to the square root of their product . Given the proportion a : b = b : c . ( 1 ) • To Prove b = Vac . Proof . From ( 1 ) , b ' = ac . ( § 232 ) b = √ac . PROP . II . THEOREM . 234 ...
... proportional between two quantities is equal to the square root of their product . Given the proportion a : b = b : c . ( 1 ) • To Prove b = Vac . Proof . From ( 1 ) , b ' = ac . ( § 232 ) b = √ac . PROP . II . THEOREM . 234 ...
Σελίδα 127
... proportional between 28 and 63 . 3. Find a third proportional to & and § . 4. What is the second term of a proportion whose first , third , and fourth terms are 45 , 160 , and 224 , respectively ? PROPORTIONAL LINES . PROP . X. THEOREM ...
... proportional between 28 and 63 . 3. Find a third proportional to & and § . 4. What is the second term of a proportion whose first , third , and fourth terms are 45 , 160 , and 224 , respectively ? PROPORTIONAL LINES . PROP . X. THEOREM ...
Σελίδα 128
... proportionally if A E B C F D AE BE AB CF DF CD PROP . XI . THEOREM . 244. A parallel to one side of a triangle divides the other two sides proportionally . Case I. When the segments of each side are commensu- rable . D E B C Given , in ...
... proportionally if A E B C F D AE BE AB CF DF CD PROP . XI . THEOREM . 244. A parallel to one side of a triangle divides the other two sides proportionally . Case I. When the segments of each side are commensu- rable . D E B C Given , in ...
Σελίδα 130
... proportionally . PROP . XII . THEOREM . 248. ( Converse of Prop . XI . ) A line which divides two sides of a triangle proportionally is parallel to the third side . A D F E B Given , in △ ABC , line DE meeting AB and AC at D and E ...
... proportionally . PROP . XII . THEOREM . 248. ( Converse of Prop . XI . ) A line which divides two sides of a triangle proportionally is parallel to the third side . A D F E B Given , in △ ABC , line DE meeting AB and AC at D and E ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² adjacent angles altitude apothem approach the limit area ABC axis base and altitude BC² bisector bisects centre chord circle circumference circumscribed coincide cone of revolution Converse of Prop diagonals diameter diedral angle distance Draw line equally distant equilateral equivalent exterior angle faces Find the area frustum Given line given point Hence homologous homologous sides hypotenuse intersecting isosceles triangle lateral area lateral edges line drawn line joining middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedral polyedron prism pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles right triangle segment side BC similar slant height spherical polygon spherical triangle square tangent tetraedron THEOREM trapezoid triangle ABC triangular prism triedral vertex vertices volume Whence
Δημοφιλή αποσπάσματα
Σελίδα 371 - A zone is a portion of the surface of a sphere included between two parallel planes.
Σελίδα 49 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...
Σελίδα 261 - The projection of a point on a plane is the foot of the perpendicular drawn from the point to the plane.
Σελίδα 336 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Σελίδα 73 - A chord is a straight line joining the extremities of an arc ; as AB.
Σελίδα 328 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 205 - S' denote the areas of two © whose radii are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.
Σελίδα 170 - 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.
Σελίδα 224 - The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars.
Σελίδα 325 - A right circular cone may be generated by the revolution of a right triangle about one of its legs as an axis.