Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. SmithRivingtons, 1872 - 349 sider |
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Side 142
... TANGENT to , or to touch , a circle , when it meets and , being produced , does not cut the circle . From this definition it follows that the tangent meets the circle in one point only , for if it met the circle in two points it would ...
... TANGENT to , or to touch , a circle , when it meets and , being produced , does not cut the circle . From this definition it follows that the tangent meets the circle in one point only , for if it met the circle in two points it would ...
Side 143
... tangent to the circle . Ø B Let ABC be a O , of which the centre is O , and the diameter AOB . Through B draw DE at right angles to AOB . I. 11 . Then must DE be a tangent to the O. Take any point P in DE , and join OP . Then ...
... tangent to the circle . Ø B Let ABC be a O , of which the centre is O , and the diameter AOB . Through B draw DE at right angles to AOB . I. 11 . Then must DE be a tangent to the O. Take any point P in DE , and join OP . Then ...
Side 144
... tangent to the ○ BCD . I. 16 . Similarly it may be shewn that AD is a tangent to ✪ BCD . Next , let the given pt . be on the Oce of the O , as B. Then , if BA be drawn to the radius OB , BA is a tangent to the C at B. I. 16 . Q. E. D. ...
... tangent to the ○ BCD . I. 16 . Similarly it may be shewn that AD is a tangent to ✪ BCD . Next , let the given pt . be on the Oce of the O , as B. Then , if BA be drawn to the radius OB , BA is a tangent to the C at B. I. 16 . Q. E. D. ...
Side 162
... tangents is double of the angle contained by the line joining the points of contact , and the diameter drawn through one of them . Ex . 4. The vertical angle of any oblique - angled triangle inscribed in a circle is greater or less than ...
... tangents is double of the angle contained by the line joining the points of contact , and the diameter drawn through one of them . Ex . 4. The vertical angle of any oblique - angled triangle inscribed in a circle is greater or less than ...
Side 164
... tangent to the ABH . III . 16 . And the chord AB is drawn from the pt . of contact A , .. 4 BAD = 4 in segment AHB ... tangents at P and Q is equal to the angle between the tangents at A. Ex . 2. From two given points on the same side of ...
... tangent to the ABH . III . 16 . And the chord AB is drawn from the pt . of contact A , .. 4 BAD = 4 in segment AHB ... tangents at P and Q is equal to the angle between the tangents at A. Ex . 2. From two given points on the same side of ...
Andre utgaver - Vis alle
Elements of geometry, containing books i. to vi.and portions of books xi ... Euclides,James Hamblin SMITH Uten tilgangsbegrensning - 1876 |
Elements of Geometry, Containing Books I. to Vi.And Portions of Books Xi ... James Hamblin Smith,Euclides Ingen forhåndsvisning tilgjengelig - 2022 |
Elements of Geometry, Containing Books I. to VI.and Portions of Books XI ... James Hamblin Smith,Euclides Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
ABCD AC=DF angles equal angular points base BC bisecting the angle centre chord circumference coincide diagonals diameter divided equal angles equal circles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given circle given line given point given st given straight line greater Hence hypotenuse inscribed isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram perpendicular polygon produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rectangle contained Reflex Angles required to describe rhombus right angles segment semicircle shew shewn straight line joining subtended sum of sqq Take any pt tangent THEOREM trapezium triangle ABC triangles are equal vertex vertical angle
Populære avsnitt
Side 52 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Side 17 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz.
Side 167 - 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.
Side 69 - The complements of the parallelograms which are about the diameter of any parallelogram, are equal to one another. Let ABCD be a parallelogram, of which the diameter is AC...
Side 106 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Side 88 - If a straight line be bisected, and produced to any point, the square on the whole line thus produced, and the square on the part of it produced, are together double of the square on half the line bisected; and of the square on the line made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to the point D. Then the squares on AD, DB, shall be double of the squares on AC, CD.
Side 78 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 91 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Side 5 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.