Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, Μέρος 21872 |
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Αποτελέσματα 1 - 5 από τα 19.
Σελίδα 121
... less , or greater than , the radius of the circle . DEFINITIONS . I. A straight line , as PQ , drawn so as to cut a circle ABCD , is called a SECANT . B P D That such a line can only meet the circumference in two points may be shewn ...
... less , or greater than , the radius of the circle . DEFINITIONS . I. A straight line , as PQ , drawn so as to cut a circle ABCD , is called a SECANT . B P D That such a line can only meet the circumference in two points may be shewn ...
Σελίδα 124
... less than the radius of the © , and .. D lies within the O. And the same may be shewn of any other pt . in AB . .. AB lies entirely within the . Q. E. D. PROPOSITION III . THEOREM . If a straight line , 124 EUCLID'S ELEMENTS .
... less than the radius of the © , and .. D lies within the O. And the same may be shewn of any other pt . in AB . .. AB lies entirely within the . Q. E. D. PROPOSITION III . THEOREM . If a straight line , 124 EUCLID'S ELEMENTS .
Σελίδα 130
... less than any other line that can be drawn from P to the circumference . Ex . 2. Shew that PB continually decreases , as B passes from A to D. Ex . 3. Shew that two lines , but not three , that shall be equal , can be drawn from P to ...
... less than any other line that can be drawn from P to the circumference . Ex . 2. Shew that PB continually decreases , as B passes from A to D. Ex . 3. Shew that two lines , but not three , that shall be equal , can be drawn from P to ...
Σελίδα 131
... less than the sum of PO , OB , .. PB is less than the sum of PO , OC ; .. PB is less than PC . I. 20 . Ex . 1. Shew that PB continually increases as B passes C. from A to Ex . 2. Shew that from P two lines , but not three , that shall ...
... less than the sum of PO , OB , .. PB is less than the sum of PO , OC ; .. PB is less than PC . I. 20 . Ex . 1. Shew that PB continually increases as B passes C. from A to Ex . 2. Shew that from P two lines , but not three , that shall ...
Σελίδα 137
... less than OA and AP together . But OP is less than OA and AP together , which is impossible ; I. 20 . ..the centre of O ADE cannot lie out of AE . Q. E. D. Ex . Three circles touch one another externally , whose centres are A , B , C ...
... less than OA and AP together . But OP is less than OA and AP together , which is impossible ; I. 20 . ..the centre of O ADE cannot lie out of AE . Q. E. D. Ex . Three circles touch one another externally , whose centres are A , B , C ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angular points bisect the angle centre of ADE chord AC circle be described circle described circles cut circles intersect circles touch circumference coincide cutting the circle Describe a circle diagonals diameter draw equal circles equiangular equilateral triangle given circle given line given point given square given straight line isosceles triangle Join OA Let ABC line be drawn line drawn meet the Oce middle points opposite sides parallel parallelogram pass perpendicular point of contact produced prove Q. E. D. Ex Q. E. F. PROPOSITION quadrilateral quadrilateral figure rect rectangle contained reflex angle regular pentagon regular polygon required to inscribe rhombus right angles segment ABC semicircle shew shewn straight line joining subtended sum of 48 tangents THEOREM touch the circle triangle ABC vertex
Δημοφιλή αποσπάσματα
Σελίδα 152 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.
Σελίδα 168 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 161 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 132 - If a point be taken within a circle, from which there fall more than two equal straight lines to the circumference, that point is the centre of the circle. Let...
Σελίδα 163 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Σελίδα 177 - IN a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw (1 7. 3.) the straight line G AH touching the circle in the point A, and. at the point A, in the straight line AH, make (23.
Σελίδα 184 - ABD is described, having each of the angles at the base double of the third angle.
Σελίδα 207 - Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible. let the two similar segments of circles, viz. ACB' ADB be upon the same side of the same straight line AB, not coinciding with one another.
Σελίδα 203 - If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.
Σελίδα 183 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.