Text-book of Elementary Plane GeometrySampson Low, Marston, Searle & Rivington, 1880 - 73 σελίδες |
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Σελίδα 18
... altitude must coincide with one of the sides , if one of the angles at the base is a right angle , and fall out ... altitude , median line and the line bisecting the vertical angle , coincide in one line ; for if the altitude did not ...
... altitude must coincide with one of the sides , if one of the angles at the base is a right angle , and fall out ... altitude , median line and the line bisecting the vertical angle , coincide in one line ; for if the altitude did not ...
Σελίδα 21
... altitude from the vertex divides an isosceles triangle symmetrically , that every diameter divides a circle symmetrically , & c . A a D C B b d When two pair of figures lie symmetrically with regard to the same line , their points of ...
... altitude from the vertex divides an isosceles triangle symmetrically , that every diameter divides a circle symmetrically , & c . A a D C B b d When two pair of figures lie symmetrically with regard to the same line , their points of ...
Σελίδα 32
... altitude from an extremity of the base . 72. Which parallelograms can be inscribed in a circle , and which can be circumscribed ? 73. Prove that a polygon can be constructed , when all its parts are known , except three , which follow ...
... altitude from an extremity of the base . 72. Which parallelograms can be inscribed in a circle , and which can be circumscribed ? 73. Prove that a polygon can be constructed , when all its parts are known , except three , which follow ...
Σελίδα 33
... altitude of the triangle . 79. In a parallelogram a diagonal is drawn , and through a point in this , lines parallel ... altitude of a triangle , reckoned from the point of intersection of the altitudes to the foot , is equal to the ...
... altitude of the triangle . 79. In a parallelogram a diagonal is drawn , and through a point in this , lines parallel ... altitude of a triangle , reckoned from the point of intersection of the altitudes to the foot , is equal to the ...
Σελίδα 34
... altitudes of a triangle bisect the angles of another triangle , having its angular points at the feet of the altitudes . ( Find in the figure systems of four points lying in the circumference of the same circle ) . Prove by the help of ...
... altitudes of a triangle bisect the angles of another triangle , having its angular points at the feet of the altitudes . ( Find in the figure systems of four points lying in the circumference of the same circle ) . Prove by the help of ...
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...