Numerical Problems in Plane Geometry with Metric and Logarithmic TablesLongmans, Green and Company, 1897 - 144 σελίδες |
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Σελίδα 18
... altitude in the second . 11. The sides of a are 4m 6dm , 6m 1dın , and 8m ; the homologous sides of a similar are a , 305cm , c ; find a and c . 12. In the △ A B C and A ' B ' C ' , A = 59 ° = A ' , b = 3 feet 6 inches , c = 13 feet ...
... altitude in the second . 11. The sides of a are 4m 6dm , 6m 1dın , and 8m ; the homologous sides of a similar are a , 305cm , c ; find a and c . 12. In the △ A B C and A ' B ' C ' , A = 59 ° = A ' , b = 3 feet 6 inches , c = 13 feet ...
Σελίδα 19
... altitudes of a A = 1.5m ; find the homologous altitude of a similar △ , if the perimeters of the two △ are respectively 15 feet and 24 feet . 16. A series of straight lines passing through the point O intercept segments , on one of ...
... altitudes of a A = 1.5m ; find the homologous altitude of a similar △ , if the perimeters of the two △ are respectively 15 feet and 24 feet . 16. A series of straight lines passing through the point O intercept segments , on one of ...
Σελίδα 20
... altitude of a △ in terms of its sides . 44 FIG . 6 . B4 α FIG . 7 . ( 1 ) h2 = c2 - B D. ( The square of either leg of a right A is equal to the square of the hypotenuse minus the square of the other leg . ) b2 = a2 + c2 2a x BD ...
... altitude of a △ in terms of its sides . 44 FIG . 6 . B4 α FIG . 7 . ( 1 ) h2 = c2 - B D. ( The square of either leg of a right A is equal to the square of the hypotenuse minus the square of the other leg . ) b2 = a2 + c2 2a x BD ...
Σελίδα 21
... and h " representing the altitude of the upon b and c , respectively . 25. To find the radius of the circumscribed in terms of the sides of the △ . FIG . 8 . a FIG . 9 . ac = 2Rx B D. ( Fig . 8. ) GEOMETRY - NUMERICAL PROBLEMS . 21.
... and h " representing the altitude of the upon b and c , respectively . 25. To find the radius of the circumscribed in terms of the sides of the △ . FIG . 8 . a FIG . 9 . ac = 2Rx B D. ( Fig . 8. ) GEOMETRY - NUMERICAL PROBLEMS . 21.
Σελίδα 22
... altitude to the third side . ) 2 But by 24 , B D = b √ s ( s — a ) ( s — b ) ( s — c ) ' 4R Hence ac = b √s ( s — a ) ( s — b ) ( s — c ) ' and R = a b c 4s ( s - a ) ( s — b ) ( s — c ) 26. To find the bisectors of the of a △ in ...
... altitude to the third side . ) 2 But by 24 , B D = b √ s ( s — a ) ( s — b ) ( s — c ) ' 4R Hence ac = b √s ( s — a ) ( s — b ) ( s — c ) ' and R = a b c 4s ( s - a ) ( s — b ) ( s — c ) 26. To find the bisectors of the of a △ in ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
acres adjacent sides ALGEBRA altitude angle is equal apothem arc intercepted arc subtended bisect bisector centre chord circum circumscribed College cologarithm construct a triangle decagon diagonals divided dodecagon equiangular polygon equilateral triangle escribed exterior extreme and mean figure Find the area find the length Find the number Find the radius Find the side GEOMETRY given line given point given triangle homologous sides hypotenuse intercepted arcs interior angles intersect isosceles triangle joining the middle June line joining lines drawn logarithm mantissa mean proportional metres middle points miles non-parallel sides opposite sides parallel sides parallelogram pentagon perimeter perpendicular PLANE GEOMETRY points of contact problems Prove quadrilateral radii rectangle regular hexagon regular inscribed regular polygon respectively rhombus right angles right triangle scribed secant Show similar triangles square equivalent square feet straight line tangent Tech terior third side trapezoid triangle is equal University vertex vertices yards
Δημοφιλή αποσπάσματα
Σελίδα 102 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Σελίδα 80 - If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Σελίδα 94 - 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'.
Σελίδα 102 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Σελίδα 141 - When the length of the primary unit of this system was determined it was supposed to be one ten-millionth of the distance from the equator to the pole.
Σελίδα 66 - OA will be 13 inches. 3. Prove that an angle formed by a tangent and a chord drawn through its point of contact is the supplement of any angle inscribed in the segment cut off by the chord. What is the locus of the centre of a circumference of given radius which cuts at right angles a given circumference? 4. Show that the areas of similar triangles are to each other as the squares of the homologous sides. 5. Prove that the square described upon the altitude of an equilateral triangle has an area...
Σελίδα 69 - 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.
Σελίδα 75 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Σελίδα 89 - The exterior angles of a polygon, made by producing each of its sides in succession, are together equal to four right angles.
Σελίδα 104 - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.