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

### From inside the book

Results 1-5 of 33

Page 90

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**submultiple**of a greater , when the less measures the greater . 2. A greater magnitude is called a multiple of a ...**submultiple**whatsoever of the first is contained in the second , as often as an equi -**submultiple**of the third is ... Page 92

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**submultiples**, are equal , 3. A multiple or**submultiple**of a greater magnitude is greater than the equi - multiple or equi -**submultiple**of a less . 4. That magnitude , of which a multiple or**submulti**- ple is greater than the equi ... Page 94

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**submultiple**of the first be always contained in the third as often as an equi -**submultiple**of the second is contained in the fourth , the third is equal to the fourth . PROP . II . THEOR . If there be four magnitudes ( A , B , CD and ... Page 95

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**submultiple**of any third magnitude ( E ) , which is con- tained in the greater oftener than in the less . Let mB be the excess of AB above CD , take e a**submultiple**of E less than mB , and since Am is equal to CD , è is contained in Am ... Page 96

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**submultiple**of CD , take it away from AB as often as it is contained in CD , and let mB be the re- ( 1 ) Hypoth . mainder ( 1 ) ; Am is equal to CD because they are equi- multiples of e , therefore AB is greater than CD . Fig . 5 . But ...### 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.