The First Six Books with NotesR. Milliken, 1822 - 179 pages |
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Page 57
... circumference , those which make egual angles with the line passing through the centre are equal . Of those lines which are incident upon the concave circumference , the greatest is that which passes through the centre . Of the rest ...
... circumference , those which make egual angles with the line passing through the centre are equal . Of those lines which are incident upon the concave circumference , the greatest is that which passes through the centre . Of the rest ...
Page 58
... circumference , that line AY which passes through the centre is greater than any other AX . Draw ZX , and ZY is equal to ZX ( 5 ) , therefore if AZ be added to both , AY shall be equal to AZ and ZX taken together , but AZ and ZX ...
... circumference , that line AY which passes through the centre is greater than any other AX . Draw ZX , and ZY is equal to ZX ( 5 ) , therefore if AZ be added to both , AY shall be equal to AZ and ZX taken together , but AZ and ZX ...
Page 59
... circumference . First . If any three lines be drawn , either one of them shall pass through the centre , and therefore be either greater or less than either of the others ( 12 ) , or two ( 12 ) Part . 2 must be at the same side of the ...
... circumference . First . If any three lines be drawn , either one of them shall pass through the centre , and therefore be either greater or less than either of the others ( 12 ) , or two ( 12 ) Part . 2 must be at the same side of the ...
Page 64
... 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 the circle again . Cor . 1. From this proposition is immediately de- duced a ...
... 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 the circle again . Cor . 1. From this proposition is immediately de- duced a ...
Page 66
... circumference , when they have the same part of the circumference for their base . See N. Fig . 27 . 1. Let one side of the angle at the circumference pass through the centre ; because in the triangle DCB , the sides DC and CB are equal ...
... circumference , when they have the same part of the circumference for their base . See N. Fig . 27 . 1. Let one side of the angle at the circumference pass through the centre ; because in the triangle DCB , the sides DC and CB are 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.