The First Six Books with NotesR. Milliken, 1822 - 179 pages |
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Page 64
... tangent can only meet the circle in one point , and that at each point of the circumference there is only one tangent . Schol . 2. It is also evident , that the right line , which makes at B an acute angle , however great , must meet ...
... tangent can only meet the circle in one point , and that at each point of the circumference there is only one tangent . Schol . 2. It is also evident , that the right line , which makes at B an acute angle , however great , must meet ...
Page 65
... tangent to the circle . Let C be the centre of the given circle , and from the centre C with the radius CA , describe a circle CAE ; draw CA which meets the circle in the point F , and draw through the point F the line FE per ...
... tangent to the circle . Let C be the centre of the given circle , and from the centre C with the radius CA , describe a circle CAE ; draw CA which meets the circle in the point F , and draw through the point F the line FE per ...
Page 66
... tangent to a circle , the right line ( BA ) drawn perpendicular to it from the point of contact , passes through the centre of the circle . For , if it be possible , let the centre Z be without the line BA and draw ZB . Because the ...
... tangent to a circle , the right line ( BA ) drawn perpendicular to it from the point of contact , passes through the centre of the circle . For , if it be possible , let the centre Z be without the line BA and draw ZB . Because the ...
Page 72
... angle ABC in a semi- circle is right . Cor . 2. Hence also can be drawn a tangent to a circle from a given point without it : draw a right line from the given point to the centre of the circle 72 Elements of Euclid .
... angle ABC in a semi- circle is right . Cor . 2. Hence also can be drawn a tangent to a circle from a given point without it : draw a right line from the given point to the centre of the circle 72 Elements of Euclid .
Page 73
... tangent ; for it is perpendicular to the radius draw to the point where it meets the circle , because the angle in a semicircle is a right angle . PROP . XXXII . THEOR . If a right line ( EF ) be a tangent to a circle and Fig . 44 ...
... tangent ; for it is perpendicular to the radius draw to the point where it meets the circle , because the angle in a semicircle is a right angle . PROP . XXXII . THEOR . If a right line ( EF ) be a tangent to a circle and Fig . 44 ...
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Common terms and phrases
absurd AC and BD AC and CB AC are equal alternate angles angle ABC angle ACD angle BAC angle equal base bisected centre circumference CKMB Constr constructed contained in CD demonstrated double the rectangle double the square equal angles equal sides equal to AC equal to double equi equi-multiples equi-submultiples equiangular Euclid evident fore four magnitudes proportional four right angles given angle given circle given line given right line given triangle half a right Hypoth inscribed less line CD manner mean proportional multiple oftener parallel parallelogram perpendicular point of contact PROB produced Prop proposition radius rectangle under AC right line AB Schol segment side AC similar squares of AC submultiple taken tangent THEOR third tiple triangle ABC vertex
Popular passages
Page 145 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Page 2 - 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 : 16.
Page 28 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 22 - 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.
Page 118 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Page 146 - A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Page 168 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Page 3 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.
Page 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Page 3 - A rhombus is that which has all its sides equal, but its angles are not right angles.