A Text-book of GeometryGinn, 1888 - 386 σελίδες |
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Αποτελέσματα 1 - 5 από τα 21.
Σελίδα 5
... lines joining two points the shortest is the straight line , and the length of the straight line is called the distance between the two points . 34. A straight line determined by two points is considered DEFINITIONS . 5 STRAIGHT LINES.
... lines joining two points the shortest is the straight line , and the length of the straight line is called the distance between the two points . 34. A straight line determined by two points is considered DEFINITIONS . 5 STRAIGHT LINES.
Σελίδα 33
... shortest line that can be drawn from a point to a straight line . P C -B P Let AB be the given straight line , P the given point , PC the perpendicular , and PD any other line drawn from P to AB . To prove PC PD . Proof . Produce PC to ...
... shortest line that can be drawn from a point to a straight line . P C -B P Let AB be the given straight line , P the given point , PC the perpendicular , and PD any other line drawn from P to AB . To prove PC PD . Proof . Produce PC to ...
Σελίδα 35
... shortest distance between two points ) , BE + OE > BO . Add these inequalities , and we have CA + CE + BE + OE > OA + OE + OB . Substitute for CE + BE its equal CB , and take away OE from each side of the inequality . We have CA + CB ...
... shortest distance between two points ) , BE + OE > BO . Add these inequalities , and we have CA + CE + BE + OE > OA + OE + OB . Substitute for CE + BE its equal CB , and take away OE from each side of the inequality . We have CA + CB ...
Σελίδα 38
... shortest distance between two points ) . Substitute in this inequality DA for DB , and we have That is , CB CD + DA . CB < CA , Q. E. D. 123. Since two points determine the position of a straight 38 PLANE GEOMETRY . -BOOK I.
... shortest distance between two points ) . Substitute in this inequality DA for DB , and we have That is , CB CD + DA . CB < CA , Q. E. D. 123. Since two points determine the position of a straight 38 PLANE GEOMETRY . -BOOK I.
Σελίδα 41
... △ ABC ( Fig . 1 ) , AB + BC > AC , for a straight line is the shortest distance between two points ; and by taking away BC from both sides , AB > AC - BC , or AC - BCAB . PROPOSITION XXIII . THEOREM . 138. The sum of the TRIANGLES . 41.
... △ ABC ( Fig . 1 ) , AB + BC > AC , for a straight line is the shortest distance between two points ; and by taking away BC from both sides , AB > AC - BC , or AC - BCAB . PROPOSITION XXIII . THEOREM . 138. The sum of the TRIANGLES . 41.
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Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² acute angle altitude angles are equal apothem base bisector bisects called centre chord circumference circumscribed circumscribed circle coincide decagon diagonal diameter divide Draw equal angles equal respectively equiangular equiangular polygon equidistant equilateral triangle exterior angles feet figure Find the area given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches intersect isosceles trapezoid isosceles triangle legs length line joining measured by arc middle points number of sides parallel parallelogram perimeter perpendicular prove Proof Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radii ratio rectangle regular inscribed regular polygon rhombus right angle right triangle SCHOLIUM secant segments shortest side similar polygons straight angle subtended tangent THEOREM third side trapezoid triangle ABC triangle is equal vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 44 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 144 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 130 - If four quantities are in proportion, they are in proportion by composition; that is, 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 128 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Σελίδα 211 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Σελίδα 157 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 152 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Σελίδα 187 - ... upon the sum of two straight lines is equivalent to the sum of the squares described on the two lines plus twice their rectangle. Note. By the "rectangle of two lines" is here meant the rectangle of which the two lines are the adjacent sides.
Σελίδα 136 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Σελίδα 15 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3.