Text-book of Elementary Plane GeometrySampson Low, Marston, Searle & Rivington, 1880 - 73 σελίδες |
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Αποτελέσματα 6 - 10 από τα 13.
Σελίδα 23
... less than their difference , when one circle lies within the other . If the chord , which the circles A have in common , becomes infinitely small , so that the points of intersection coincide in one point , this is called a point of ...
... less than their difference , when one circle lies within the other . If the chord , which the circles A have in common , becomes infinitely small , so that the points of intersection coincide in one point , this is called a point of ...
Σελίδα 24
... point of intersection of two circles , with centres A and B , and with the other given sides as radii . The prob- lem is possible , when the circles cut each other , therefore , A B A when the one side is less than 24.
... point of intersection of two circles , with centres A and B , and with the other given sides as radii . The prob- lem is possible , when the circles cut each other , therefore , A B A when the one side is less than 24.
Σελίδα 25
... less than the perpendicular BD , the circle will not cut AD , and the problem is impossible . b ) If BC = BD , the circle will touch AD at D , and there will be one solution , namely , the right - angled triangle ADB . c ) If BC > BD ...
... less than the perpendicular BD , the circle will not cut AD , and the problem is impossible . b ) If BC = BD , the circle will touch AD at D , and there will be one solution , namely , the right - angled triangle ADB . c ) If BC > BD ...
Σελίδα 26
... less than 2R . As there only is one solution , two triangles are congruent , when they have one side and the angles at that side respectively equal . Y x A 63. To construct a triangle , having given a side , an angle at the side , and ...
... less than 2R . As there only is one solution , two triangles are congruent , when they have one side and the angles at that side respectively equal . Y x A 63. To construct a triangle , having given a side , an angle at the side , and ...
Σελίδα 38
... less than I 9 but this fraction can be made as small as we please , for q can be taken as great as we please ; but when the difference between the ratios is less than any ever so small quantity , it must be zero , and the ratios ...
... less than I 9 but this fraction can be made as small as we please , for q can be taken as great as we please ; but when the difference between the ratios is less than any ever so small quantity , it must be zero , and the ratios ...
Άλλες εκδόσεις - Προβολή όλων
Text-Book of Elementary Plane Geometry Julius Petersen,R Steenberg Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Text-Book of Elementary Plane Geometry Julius Petersen,R Steenberg Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Text-Book of Elementary Plane Geometry .. Julius Petersen,R Steenberg Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles adjacent side altitude angle equal angular points base bisecting the angle called chord circle touches circles cut circumference circumscribed coincide Construct a triangle containing the right corresponding lines corresponding points describe a circle diagonals diameter divided draw equilateral triangle given angle given circle given line given point given side half the perimeter hypothenuse inscribed circle isosceles triangle legs line bisecting line is drawn line joining line of centres mean proportional middle point number of sides opposite angle opposite side parallelogram pendicular perimeter perpendicular point of intersection points of contact points of division proposition Prove quadrilateral radii ratio rectangle regular polygon rhombus right angle right-angled triangle secant semicircle Shew sided figure sides containing similar square straight line tangent third side trapezium triangle ABC triangles are congruent vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 13 - In a right triangle, the perpendicular from the vertex of the right angle to the hypotenuse is a mean proportional between the segments of the hypotenuse: p2 = mn. Any two similar figures, in the plane or in space, can be placed in " perspective," that is, so that lines joining corresponding points of the two figures will pass through a common point.
Σελίδα 52 - The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair.
Σελίδα 25 - Each side of a triangle is smaller than the sum of the other two, and greater than their difference. The first part of this theorem is an immediate consequence of the Axiom of Distance (54) ; that is, AC < AB + BC. Subtract AB from both members of this inequality, and AC — AB < BC. That is, BC is greater than the difference of the other sides. Prove the same for each of the other sides.
Σελίδα 66 - The area of any polygon circumscribing a circle is equal to half the product of the radius of the circle, and the perimeter of the polygon. (Divide the polygon into triangles, with the centre for vertex.) tEx.
Σελίδα 46 - If two circles touch each other, and also touch a given straight line, the part of the straight line between the points of contact is a mean proportional between the diameters of the circles.
Σελίδα 14 - Ьs + cs - 2Ьc cos A, and apply it to prove that if the straight line which bisects the vertical angle of a triangle also bisects the base, then the triangle must be isosceles. 9. Find the area of a triangle in terms of the sides. 10. Find the radius of the circle which touches one side of a triangle and the two other sides produced.
Σελίδα 57 - ... as any homologous altitudes. 549. EXERCISE. The perimeters of similar triangles are to each other as any homologous medians. 550. EXERCISE. The perimeters of two similar polygons are 78 and 65 ; a side of the first is 9, find the homologous side of the second. 551. DEFINITION. A line is divided in extreme and mean ratio when it is divided into two parts so that one segment is a mean proportional between the whole line and the other segment. PROPOSITION XXVIII. PROBLEM 552. To divide a line in...
Σελίδα 32 - From any point in the base of an isosceles triangle perpendiculars are drawn to the sides ; prove their sum to be equal to the perpendicular drawn from either basal vertex to the opposite side.
Σελίδα 61 - The lengths of the circumferences of two circles are to each other as the radii.
Σελίδα 24 - ... of the other two sides ; to construct the triangle. 77. Given the base and the sum of the two other sides of a triangle, construct it so that the line which bisects the vertical angle shall be parallel to a given line. V. 78. From a given point without a given straight line, to draw a line making an angle with the given line equal to a given rectilineal angle. 79. Through a given point A, draw a straight line A...