Plane GeometrySilver, Burdett, 1896 - 253 Seiten |
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Seite 73
... approach . Expressed in general terms , if a and b are incommensurable , their ratio would be indicated by dividing b into n equal parts ; a will contain one of these parts a certain number of times , such as m , with a remainder less ...
... approach . Expressed in general terms , if a and b are incommensurable , their ratio would be indicated by dividing b into n equal parts ; a will contain one of these parts a certain number of times , such as m , with a remainder less ...
Seite 74
... approach indefinitely its limit . 171. If a variable is increasing , it approaches a superior limit ; if decreasing , an inferior limit . A P P ' P. " P " " B Thus , a point may be supposed to move along a straight line from A toward B ...
... approach indefinitely its limit . 171. If a variable is increasing , it approaches a superior limit ; if decreasing , an inferior limit . A P P ' P. " P " " B Thus , a point may be supposed to move along a straight line from A toward B ...
Seite 75
... approaches zero as a limit , each base angle approaches a right angle as a limit , and the two legs in their length approach infinity , and in their direction approach parallelism . PROPOSITION X 172. Theorem . If two variables are ...
... approaches zero as a limit , each base angle approaches a right angle as a limit , and the two legs in their length approach infinity , and in their direction approach parallelism . PROPOSITION X 172. Theorem . If two variables are ...
Seite 76
... approaches a limit , their limits are equal . Appl . Cons . Dem . A 3 D 1L 2 AC and 13 are variables approaching ... approach 0 . X If is a variable equal to 3 , the successive values of the У variable will be x x X X X X 19 9 y 3y 9y 27 ...
... approaches a limit , their limits are equal . Appl . Cons . Dem . A 3 D 1L 2 AC and 13 are variables approaching ... approach 0 . X If is a variable equal to 3 , the successive values of the У variable will be x x X X X X 19 9 y 3y 9y 27 ...
Seite 148
... approaches the radius of the circle as a limit . 2. The perimeters of both polygons approach the cir- cumference of the circle as a limit . 3. The polygons approach the circle as a limit . L A E B F K H 1. Prove CO = limit of FO . Appl ...
... approaches the radius of the circle as a limit . 2. The perimeters of both polygons approach the cir- cumference of the circle as a limit . 3. The polygons approach the circle as a limit . L A E B F K H 1. Prove CO = limit of FO . Appl ...
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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.