Text-book of Elementary Plane GeometrySampson Low, Marston, Searle & Rivington, 1880 - 73 σελίδες |
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Αποτελέσματα 1 - 5 από τα 13.
Σελίδα 3
... placed on each other , so that they cover one another ; the parts which then . coincide are called corresponding . The sign for congruence Circles with equal radii are congruent . is . 9. That which is given in a proposition is called ...
... placed on each other , so that they cover one another ; the parts which then . coincide are called corresponding . The sign for congruence Circles with equal radii are congruent . is . 9. That which is given in a proposition is called ...
Σελίδα 5
... placed on one of the sides of the polygon , from thence turn- ed on to the next side and so on , till it again falls on the first side , it will by degrees have turned through all the exterior angles of the polygon ; but it has thereby ...
... placed on one of the sides of the polygon , from thence turn- ed on to the next side and so on , till it again falls on the first side , it will by degrees have turned through all the exterior angles of the polygon ; but it has thereby ...
Σελίδα 6
... placed on itself in an inverted position , so that B covers itself , BC falls along BA , and BA along BC , then A must fall in C , and C in A , and consequently AC coincides with CA ; as the angles A and C thereby coincide they are ...
... placed on itself in an inverted position , so that B covers itself , BC falls along BA , and BA along BC , then A must fall in C , and C in A , and consequently AC coincides with CA ; as the angles A and C thereby coincide they are ...
Σελίδα 18
... placed , so that the equal sides AB coincide , further AD AC ; a perpendicular on the middle of CD will pass through A ( 45 , last piece ) ; therefore CB > DB . ( 45 ) . - 47. The altitude of a triangle is a line , drawn from an angular ...
... placed , so that the equal sides AB coincide , further AD AC ; a perpendicular on the middle of CD will pass through A ( 45 , last piece ) ; therefore CB > DB . ( 45 ) . - 47. The altitude of a triangle is a line , drawn from an angular ...
Σελίδα 21
... placed , that it is found by dropping a perpendicular from the first point on to the line , and producing it equally far on the other side ; thus A corresponds to a , B to h , & c . Symmet- rical figures are congruent , as the one , by ...
... placed , that it is found by dropping a perpendicular from the first point on to the line , and producing it equally far on the other side ; thus A corresponds to a , B to h , & c . Symmet- rical figures are congruent , as the one , by ...
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.