The First Six Books with NotesR. Milliken, 1822 - 179 pages |
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Page 4
... constructed upon the given line ; but it is also equilateral , for the right line AC is equal to AB , as they are ... construct an equilateral triangle ADB ( 2 ) . From ( 3 ) Post . 3. the centre B with the radius BC describe a circle ...
... constructed upon the given line ; but it is also equilateral , for the right line AC is equal to AB , as they are ... construct an equilateral triangle ADB ( 2 ) . From ( 3 ) Post . 3. the centre B with the radius BC describe a circle ...
Page 5
... constructed . PROP . III . PROB . From the greater of two right lines ( AB and CF , ) Fig . 14 . to cut off a part equal to the less . See N. 14 From either extremity A of the greater line draw AD equal to FC the less of the given right ...
... constructed . PROP . III . PROB . From the greater of two right lines ( AB and CF , ) Fig . 14 . to cut off a part equal to the less . See N. 14 From either extremity A of the greater line draw AD equal to FC the less of the given right ...
Page 7
... constructed two triangles , ( ACB , and 20 . ADB , whose conterminous sides , ( AC and AD , BC and BD ) are equal . Ifit be possible , let the two triangles be constructed , Fig . 18 . and first let the vertex of each of the triangles ...
... constructed two triangles , ( ACB , and 20 . ADB , whose conterminous sides , ( AC and AD , BC and BD ) are equal . Ifit be possible , let the two triangles be constructed , Fig . 18 . and first let the vertex of each of the triangles ...
Page 8
... constructed upon the same right line cannot have their conterminous sides equal , if the vertex of one of them is within the other . Thirdly . Let the vertex D of one triangle be on the side of the other AC , and it is evident that the ...
... constructed upon the same right line cannot have their conterminous sides equal , if the vertex of one of them is within the other . Thirdly . Let the vertex D of one triangle be on the side of the other AC , and it is evident that the ...
Page 15
... constructed equal to a given one , by constructing a triangle whose sides shall be equal to the sides of the given , for this triangle is equal to the given one ( 3 ) . PROP . XXIII . PROB . ( 3 ) Schol . Prop . 8 . At a given point ( B ) ...
... constructed equal to a given one , by constructing a triangle whose sides shall be equal to the sides of the given , for this triangle is equal to the given one ( 3 ) . PROP . XXIII . PROB . ( 3 ) Schol . Prop . 8 . At a given point ( B ) ...
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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.