Text-book of Elementary Plane GeometrySampson Low, Marston, Searle & Rivington, 1880 - 73 σελίδες |
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Σελίδα 1
... formed . Thus , if we examine a piece of chalk , we might ask about its origin and occurrence , its specific gravity and colour , the combination of its elements , its form , & c . , and these questions will be answered respectively by ...
... formed . Thus , if we examine a piece of chalk , we might ask about its origin and occurrence , its specific gravity and colour , the combination of its elements , its form , & c . , and these questions will be answered respectively by ...
Σελίδα 5
... formed by the inter- section of two lines can therefore be found , when the one is known ; for example , if a = 45 ° , then also a ' = 45 ° , b = b ' = 135 ° . 16. The sum of the exterior angles of a polygon is 4R . For if a line be ...
... formed by the inter- section of two lines can therefore be found , when the one is known ; for example , if a = 45 ° , then also a ' = 45 ° , b = b ' = 135 ° . 16. The sum of the exterior angles of a polygon is 4R . For if a line be ...
Σελίδα 10
... formed by joining the points of contact is isosceles , as the angles at the base are measured by the same arc ( 25 ) . ( See the last figure to 28 ) . 30. A tangent is perpendicular to the radius to the point of contact , for the angle ...
... formed by joining the points of contact is isosceles , as the angles at the base are measured by the same arc ( 25 ) . ( See the last figure to 28 ) . 30. A tangent is perpendicular to the radius to the point of contact , for the angle ...
Σελίδα 11
... formed by an intersecting line , it is evident that through one given point , there can only be drawn one line parallel to a given line , and that When two lines are parallel to the same third line , they are parallel to one another ...
... formed by an intersecting line , it is evident that through one given point , there can only be drawn one line parallel to a given line , and that When two lines are parallel to the same third line , they are parallel to one another ...
Σελίδα 12
... formed , is equilateral . 13. The legs of one angle are perpendicular to the legs of another angle ; prove that the two angles are equal or supplementary . 14. One of the angles at the base of an isosceles triangle , whose vertical ...
... formed , is equilateral . 13. The legs of one angle are perpendicular to the legs of another angle ; prove that the two angles are equal or supplementary . 14. One of the angles at the base of an isosceles triangle , whose vertical ...
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 |
Συχνά εμφανιζόμενοι όροι και φράσεις
abc2 ABCD adjacent angles adjacent side altitude angle contained angle equal angular points base bisecting the angle centre of similitude chord circle touches circles cut circumference coincide containing the right corresponding lines corresponding points diagonals diameter draw drawn parallel equilateral triangle given angle given circles given figure 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 potense Prove quadrilateral radii ratio rectangle regular polygon required line rhombus right-angled triangle secant semicircle Shew sided figure sides containing similar square straight line tangent thereupon 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 10 - If a straight line, fatting on two other straight lines, make an exterior angle equal to the interior opposite angle on the same side of the...
Σελίδα 50 - 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 41 - ... 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 45 - The lengths of the circumferences of two circles are to each other as the radii.