The First Six Books with NotesR. Milliken, 1822 - 179 sider |
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Resultat 1-5 av 23
Side 12
... external angle ( ACD ) is greater than either of the internal opposite angles ( A or B ) . For bisect the side AC in E ( 1 ) , draw BE and ( 2 ) Prop . 3. produce it until EF be equal to BE ( 2 ) and join FC . The triangles CEF and AEB ...
... external angle ( ACD ) is greater than either of the internal opposite angles ( A or B ) . For bisect the side AC in E ( 1 ) , draw BE and ( 2 ) Prop . 3. produce it until EF be equal to BE ( 2 ) and join FC . The triangles CEF and AEB ...
Side 14
... external angle BDA is greater than the internal ( 2 ) Prop.16 . DAC ( 2 ) , but BAD is equal to DAC ( 3 ) , therefore ( 3 ) Constr . BDA is greater than BAD , and therefore the side ( 4 ) Prop . 19 BA is greater than BD ( 4 ) : in the ...
... external angle BDA is greater than the internal ( 2 ) Prop.16 . DAC ( 2 ) , but BAD is equal to DAC ( 3 ) , therefore ( 3 ) Constr . BDA is greater than BAD , and therefore the side ( 4 ) Prop . 19 BA is greater than BD ( 4 ) : in the ...
Side 15
... external angle BDC is greater than the internal DEC ( 2 ) , and for the same reason DEC ( 2 ) Prop . 18 . is greater than BAE , the angle BDC is greater than the angle BAE . PROP . XXII . PROB . Given three right lines ( A , B and C ) ...
... external angle BDC is greater than the internal DEC ( 2 ) , and for the same reason DEC ( 2 ) Prop . 18 . is greater than BAE , the angle BDC is greater than the angle BAE . PROP . XXII . PROB . Given three right lines ( A , B and C ) ...
Side 18
... external angle A EF of the triangle EGF ( 1 ) prop . 18. is greater than the internal EFG ( 1 ) , but it is also equal ( 2 ) hypoth . to it ( 2 ) , which is absurd : therefore the lines A B and CD do not meet at the side BD , and in the ...
... external angle A EF of the triangle EGF ( 1 ) prop . 18. is greater than the internal EFG ( 1 ) , but it is also equal ( 2 ) hypoth . to it ( 2 ) , which is absurd : therefore the lines A B and CD do not meet at the side BD , and in the ...
Side 19
... external angle equal to the internal and opposite angle upon the same side of the line ( EGA to GHC , and EGB to GHD ) ; or make the internal angles at the same side ( AGH and CHG , or BGH and DHG ) equal to two right angles , the two ...
... external angle equal to the internal and opposite angle upon the same side of the line ( EGA to GHC , and EGB to GHD ) ; or make the internal angles at the same side ( AGH and CHG , or BGH and DHG ) equal to two right angles , the two ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 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.
Side 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 3 - A rhombus is that which has all its sides equal, but its angles are not right angles.