A School Geometry, Μέρη 1-4Macmillan and Company, 1908 |
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Σελίδα xvi
... touch one another , the centres and the point of contact are in one straight line . 178 COR . 1. If two circles touch externally the distance be- tween their centres is equal to the sum of their radii . 178 COR . 2. If two circles touch ...
... touch one another , the centres and the point of contact are in one straight line . 178 COR . 1. If two circles touch externally the distance be- tween their centres is equal to the sum of their radii . 178 COR . 2. If two circles touch ...
Σελίδα 172
... touch it at the point at which the two intersections coincide . This point is called the point of contact . For instance : ( i ) Let a secant cut the circle at the points P and Q , and suppose it to recede from the centre , moving ...
... touch it at the point at which the two intersections coincide . This point is called the point of contact . For instance : ( i ) Let a secant cut the circle at the points P and Q , and suppose it to recede from the centre , moving ...
Σελίδα 173
... touch one another at P. Since two circles cannot intersect in more than two points , two circles which touch one another cannot have more than one point in common , namely the point of contact at which the two points of section coincide ...
... touch one another at P. Since two circles cannot intersect in more than two points , two circles which touch one another cannot have more than one point in common , namely the point of contact at which the two points of section coincide ...
Σελίδα 177
... touch a concentric circle , and find its radius . 3. The diameters of two concentric circles are respectively 100 cm ... touch a given straight line at a given point . 12. Find the locus of the centres of all circles which touch each of ...
... touch a concentric circle , and find its radius . 3. The diameters of two concentric circles are respectively 100 cm ... touch a given straight line at a given point . 12. Find the locus of the centres of all circles which touch each of ...
Σελίδα 178
... touch at the point P. It is required to prove that O , P , and Q are in one straight line . Join OP , QP . Proof . Since the given circles touch at P , they have a common tangent at that point . Suppose PT to touch both circles at P ...
... touch at the point P. It is required to prove that O , P , and Q are in one straight line . Join OP , QP . Proof . Since the given circles touch at P , they have a common tangent at that point . Suppose PT to touch both circles at P ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² adjacent angles altitude angle equal base BC bisector bisects circle of radius circle whose centre circles which touch circum-circle circumference circumscribed coincide common tangents concyclic Construct a triangle diagonals diagram diameter distance divided draw a circle equal in area equidistant escribed circles Euclid exterior angles Find the area find the locus given angle given circle given point given straight line given triangle greater Hence hypotenuse inches inscribed isosceles triangle length Let ABC meet metres middle point millimetre nine-points circle opposite sides orthocentre par¹ parallelogram pedal triangle perp PROBLEM produced Proof radii rect rectangle rectangle contained rectilineal figure required to prove respectively rhombus right angles right-angled triangle segment shew shewn straight line drawn tangent Theor Theorem trapezium triangle ABC triangles are equal vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα xi - IF two triangles have two angles of one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 44 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 190 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Σελίδα 12 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 122 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Σελίδα 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα x - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 65 - The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle (Fig.