Plane GeometryGinn, 1899 - 256 sider |
Inni boken
Resultat 1-5 av 13
Side 6
... unequal in that order . 5. If equals are taken from unequals , the remainders are unequal in the same order ; if unequals are taken from equals , the remainders are unequal in the reverse order . 6. The doubles of the same magnitude ...
... unequal in that order . 5. If equals are taken from unequals , the remainders are unequal in the same order ; if unequals are taken from equals , the remainders are unequal in the reverse order . 6. The doubles of the same magnitude ...
Side 23
... unequal segments from the foot of the perpendicu- lar , the more remote is the greater . B A- E C Let OC be perpendicular to AB , OG and OE two straight lines to AB , and CE greater than CG . To prove that OE > OG . Proof . Take CF ...
... unequal segments from the foot of the perpendicu- lar , the more remote is the greater . B A- E C Let OC be perpendicular to AB , OG and OE two straight lines to AB , and CE greater than CG . To prove that OE > OG . Proof . Take CF ...
Side 40
... unequal , the angles opposite are unequal , and the greater angle is opposite the greater side . E B In the triangle ACB , let AB be greater than AC . To prove that ACB is greater than △ B. Proof . On AB take AE equal to AC . Draw EC ...
... unequal , the angles opposite are unequal , and the greater angle is opposite the greater side . E B In the triangle ACB , let AB be greater than AC . To prove that ACB is greater than △ B. Proof . On AB take AE equal to AC . Draw EC ...
Side 41
... unequal , the sides opposite are unequal , and the greater side is opposite the greater angle . B In the triangle ACB , let the angle C be greater than the angle B. To prove that AB > AC . Proof . Now AB = AC , or AC , or > AC . But AB ...
... unequal , the sides opposite are unequal , and the greater side is opposite the greater angle . B In the triangle ACB , let the angle C be greater than the angle B. To prove that AB > AC . Proof . Now AB = AC , or AC , or > AC . But AB ...
Side 45
... unequal . Proof . for PA = 1. Δ ΟΡΑ = Δ ΟΡΒ , PB by hypothesis , and OP is common , ( two right △ are equal if their legs are equal , each to each ) . .. OA OB . 2. Since C is not in the L , CA or CB will cut the 1 . Let CA cut the 1 ...
... unequal . Proof . for PA = 1. Δ ΟΡΑ = Δ ΟΡΒ , PB by hypothesis , and OP is common , ( two right △ are equal if their legs are equal , each to each ) . .. OA OB . 2. Since C is not in the L , CA or CB will cut the 1 . Let CA cut the 1 ...
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Vanlige uttrykk og setninger
AB² ABCD AC² acute angle adjacent angles altitude angles are equal apothem arc A'B base bisector bisects called centre chord circumference circumscribed circle coincide decagon diagonals diameter divide Draw equal circles equiangular equiangular polygon equidistant equilateral triangle exterior angle feet Find the area Find the locus given angle given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches inscribed regular intercepted intersecting isosceles trapezoid isosceles triangle legs limit line drawn median middle point number of sides parallelogram perimeter perpendicular plane PROBLEM Proof prove Q. E. D. PROPOSITION quadrilateral radii radius ratio rectangle regular hexagon regular inscribed regular polygon rhombus right angle right triangle secant segments straight angle supplementary tangent THEOREM third side trapezoid triangle ABC triangle is equal variable vertex
Populære avsnitt
Side 33 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.
Side 150 - If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA = Z A', and let AB : A'B' = AC : A'C'. To prove that the A ABC and A'B'C
Side 66 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Side 191 - 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Side 169 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.
Side 32 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Side 71 - The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.
Side 156 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Side 75 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Side 162 - The sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.