The First Six Books with NotesR. Milliken, 1822 - 179 pages |
From inside the book
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Page 26
... whole , Fig . 60 . which is absurd . Therefore AF is not parallel to BH , and in the same manner it can be demonstrated , that no other line , except AD , is parallel to BH , there- fore AD is parallel to BH . PROP . XLI . THEOR . If a ...
... whole , Fig . 60 . which is absurd . Therefore AF is not parallel to BH , and in the same manner it can be demonstrated , that no other line , except AD , is parallel to BH , there- fore AD is parallel to BH . PROP . XLI . THEOR . If a ...
Page 30
... EAF is equal ( 3 ) Ax . 1 , to BÁD ( 3 ) , a part to the whole , which is absurd : therefore neither AD nor XS is greater than the other , therefore they are equal . PROP . XLVII . THEOR . In a right angled 30 Elements of Euclid .
... EAF is equal ( 3 ) Ax . 1 , to BÁD ( 3 ) , a part to the whole , which is absurd : therefore neither AD nor XS is greater than the other , therefore they are equal . PROP . XLVII . THEOR . In a right angled 30 Elements of Euclid .
Page 31
... whole DACF is equal to the sum of CZ and AX . Cor . 1. Given in numbers any two sides of a right angled triangle , the third side can be found , for it is the square root of the sum or difference of the squares of the given lines ...
... whole DACF is equal to the sum of CZ and AX . Cor . 1. Given in numbers any two sides of a right angled triangle , the third side can be found , for it is the square root of the sum or difference of the squares of the given lines ...
Page 35
... whole line is equal to the sum See N. of the rectangles under the whole ( AB ) and each of the parts ( AC , CB ) . On AB describe the square ADFB ( 1 ) , and through ( 1 ) Prop.46 C draw CE parallel to AD . The square AF is equal to the ...
... whole line is equal to the sum See N. of the rectangles under the whole ( AB ) and each of the parts ( AC , CB ) . On AB describe the square ADFB ( 1 ) , and through ( 1 ) Prop.46 C draw CE parallel to AD . The square AF is equal to the ...
Page 36
... whole line ( AB ) and either part ( AC ) is equal to the square of that part ( AC ) together with the rectangle under the parts ( AC and CB . ) On AC describe the square ADFC , and through B draw BE parallel to AD until it meet DF ...
... whole line ( AB ) and either part ( AC ) is equal to the square of that part ( AC ) together with the rectangle under the parts ( AC and CB . ) On AC describe the square ADFC , and through B draw BE parallel to AD until it meet DF ...
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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.