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

### From inside the book

Results 1-5 of 55

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**ac**- cording to the extremity of the given right line from which it is drawn , and also according to the**side**of that line on which the triangle is constructed . PROP . III . PROB . From the greater of two right lines ( AB and CF , ) Fig ... Page 6

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**side**produced , cut off AG equal to AF ( 1 ) , and join FC , GB . In the triangles FAC and GAB , the**sides**FA and**AC**...**side**FC is equal to the**side**GB ( 3 ) . Therefore in the triangles BFC , CGB , the angle BFC is equal to the angle CGB ... Page 7

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**AC**and AB ) are also equal . For if the**sides**be not equal , let one of them AB be greater than the other , and from ...**side**is taken for the base , the angles adjacent to it are equal , and therefore the**sides**which subtend them . PROP . Page 8

... AC and AD and join CD . Because the

... AC and AD and join CD . Because the

**sides AC**and AD of the triangle CAD are equal ( 6 ) , the angles ECD and FDC are ... side of the other AC , and it is evident that the**sides AC**and AD are not equal . Therefore in no case can two ... Page 9

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**side**AB and from**AC**cut Fig . 22 . 22 off AE equal to AD ( 1 ) ; draw DE and upon it des- ( 1 ) prop . 3 . cribe an equilateral triangle DFE ( 2 ) , at the**side**re- ( 2 ) prop . 1 . mote from A. The right line joining the points A and F ...### 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.