## The First Six Books with NotesR. Milliken, 1822 - 179 pages |

### From inside the book

Results 6-10 of 43

Page 15

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**BD**and DC , but BA and**AC**are greater than BE and EC , therefore BA and**AC**are greater than**BD**and DC . B 15 Because the external angle BDC is greater than the internal DEC ( 2 ) , and for the same reason DEC ( 2 ) Prop . 18 . is ... Page 18

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**AC**is equal to the side EF , and also the angle A to the angle ( 15 ) prop.4 . E ( 15 ) . Fig . 41 . Schol . It is evident that the triangles themselves are equal . Cor . 1. In an isosceles triangle ABC the right line**BD**, drawn from ... Page 22

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**AC and BD**) which join the adjacent extremities of two equal and parallel right lines ( AB and CD ) , are themselves equal and parallel . Draw the diagonal AD , and in the triangles CDA ( 1 ) Hypoth . and BAD , the sides CD and BA are ... Page 23

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**AC and BD**makes the alternate angles equal , ( 4 ) prop . 27 . and therefore the right lines**AC and BD**are parallel ( 4 ) . PROP . XXXIV . THEOR . See N. The opposite sides ( AB and CD ,**AC and BD**) of Fig 51 . a parallelogram ( AD ) ... Page 30

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**AC**perpendicular ( 1 ) and equal to it ( 2 ) , through C draw CD parallel to AB ( 3 ) , and through B draw**BD**parallel to**AC**; ABCD is the required square . ( 3 ) Prop 31 Because ABCD is a parallelogram ( 4 ) and the angle ( 4 ) ...### Other editions - View all

### 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.