The First Six Books with NotesR. Milliken, 1822 - 179 pages |
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Page 52
... arch , intercepted between the right lines that contain the angle . 9. A sector of a circle is the figure contained by two radii and the arch between them . 10. Similar segments of circles are those which con- tain equal angles . PROP ...
... arch , intercepted between the right lines that contain the angle . 9. A sector of a circle is the figure contained by two radii and the arch between them . 10. Similar segments of circles are those which con- tain equal angles . PROP ...
Page 67
... arch Fig . 32 . BD and the vertex of one of them BAD be in the circumference of the circle , the vertex of the other shall be in the same circumference . For , if it be possible , let the vertex of the other an- gle fall either without ...
... arch Fig . 32 . BD and the vertex of one of them BAD be in the circumference of the circle , the vertex of the other shall be in the same circumference . For , if it be possible , let the vertex of the other an- gle fall either without ...
Page 69
... arches , First let the given angles AOC and DHF be at the centres , draw to any points B and E in the cir- cumferences the lines AB , CB , and DE , FE , and join AC and DF . B. 1 . Because in the triangles AOC , DHF , the angles O ( 1 ) ...
... arches , First let the given angles AOC and DHF be at the centres , draw to any points B and E in the cir- cumferences the lines AB , CB , and DE , FE , and join AC and DF . B. 1 . Because in the triangles AOC , DHF , the angles O ( 1 ) ...
Page 70
... arches upon which these halves stand are equal , whence it follows that the arches on which the given angles stand are equal . PROP . XXVII . THEOR . In equal circles ( ABC , DEF ) the angles ( ABC and DEF ) which stand upon equal arches ...
... arches upon which these halves stand are equal , whence it follows that the arches on which the given angles stand are equal . PROP . XXVII . THEOR . In equal circles ( ABC , DEF ) the angles ( ABC and DEF ) which stand upon equal arches ...
Page 71
... arches from them , and the remain- B. 3 . ing arches ABC and DEF are equal . PROP . XXIX . THEOR . B. 1 . In equal circles ( ABC , DEF ) the right lines ( AC and Fig . 29 . DF ) , which subtend equal arches , are equal . If the equal ...
... arches from them , and the remain- B. 3 . ing arches ABC and DEF are equal . PROP . XXIX . THEOR . B. 1 . In equal circles ( ABC , DEF ) the right lines ( AC and Fig . 29 . DF ) , which subtend equal arches , are equal . If the equal ...
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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.