The First Six Books with NotesR. Milliken, 1822 - 179 σελίδες |
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Αποτελέσματα 1 - 5 από τα 19.
Σελίδα 18
... alternate angles equal to each other ( AEF to EFD ) , these right lines are parallel . For , if it be possible , let these lines not be parallel , but meetin G ; the external angle A EF of the triangle EGF ( 1 ) prop . 18. is greater ...
... alternate angles equal to each other ( AEF to EFD ) , these right lines are parallel . For , if it be possible , let these lines not be parallel , but meetin G ; the external angle A EF of the triangle EGF ( 1 ) prop . 18. is greater ...
Σελίδα 19
... alternate angles , therefore the right lines AB and CD are pa- rallel ( 2 ) . In the same manner the proposition can be demon- strated , if the angles EGB and GHD were given equal . ( 2 ) Prop . 27 . Next let the angles AGH and CHG ...
... alternate angles , therefore the right lines AB and CD are pa- rallel ( 2 ) . In the same manner the proposition can be demon- strated , if the angles EGB and GHD were given equal . ( 2 ) Prop . 27 . Next let the angles AGH and CHG ...
Σελίδα 20
... alternate angle GHD ( 5 ) , therefore EGB is equal to GHD ( 6 ) . In the same manner it can be demonstrated that EGA and GHC are equal . ( 5 ) Part . præc . ( 6 ) Ax . 1 . ( 6 ) Part . præc . Thirdly . The internal angles at the same ...
... alternate angle GHD ( 5 ) , therefore EGB is equal to GHD ( 6 ) . In the same manner it can be demonstrated that EGA and GHC are equal . ( 5 ) Part . præc . ( 6 ) Ax . 1 . ( 6 ) Part . præc . Thirdly . The internal angles at the same ...
Σελίδα 21
... alternate angles ECF and AFC equal , and therefore the lines are parallel ( 2 ) . PROP . XXXII . THEOR . ( 2 ) Prop . 27 . If any side ( AB ) of a triangle ( ABC ) be produced , Fig . 47 . the external angle ( FBC ) is equal to the sum ...
... alternate angles ECF and AFC equal , and therefore the lines are parallel ( 2 ) . PROP . XXXII . THEOR . ( 2 ) Prop . 27 . If any side ( AB ) of a triangle ( ABC ) be produced , Fig . 47 . the external angle ( FBC ) is equal to the sum ...
Σελίδα 22
... CD and BA are equal ( 1 ) , AD is common to both triangles , and the angle CDA isequal ( 2 ) Prop.29 . to the alternate BAD ( 2 ) , therefore the lines AC and BD are equal ( 3 ) , and also the 22 Elements of Euclid .
... CD and BA are equal ( 1 ) , AD is common to both triangles , and the angle CDA isequal ( 2 ) Prop.29 . to the alternate BAD ( 2 ) , therefore the lines AC and BD are equal ( 3 ) , and also the 22 Elements of Euclid .
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 3 - A rhombus is that which has all its sides equal, but its angles are not right angles.