The First Six Books with NotesR. Milliken, 1822 - 179 pages |
From inside the book
Results 6-10 of 18
Page 43
... divided into any two parts Fig . 17 . ( in B ) , the square of the sum of the whole line ( AC ) and either segment ( BC ) is equal to four times the rectangle under the whole line ( AC ) and that segment ( BC ) together with the square ...
... divided into any two parts Fig . 17 . ( in B ) , the square of the sum of the whole line ( AC ) and either segment ( BC ) is equal to four times the rectangle under the whole line ( AC ) and that segment ( BC ) together with the square ...
Page 74
... divided by the given ( 1 ) Prop.31 line into two semicircles , therefore each of them con- tains an angle equal to the given right angle ( 1 ) . B. 3 . Fig . 46 . If the given angle V be acute or obtuse , make with the given line AB at ...
... divided by the given ( 1 ) Prop.31 line into two semicircles , therefore each of them con- tains an angle equal to the given right angle ( 1 ) . B. 3 . Fig . 46 . If the given angle V be acute or obtuse , make with the given line AB at ...
Page 83
... divided , is half a right angle ; they are B. 1 . therefore all equal ; and therefore in the triangle AEB , as the angles EAB and EBA are equal , the sides EA and EB are equal ( 2 ) , in the same manner it can be de- ( 2 ) Prop , 6 ...
... divided , is half a right angle ; they are B. 1 . therefore all equal ; and therefore in the triangle AEB , as the angles EAB and EBA are equal , the sides EA and EB are equal ( 2 ) , in the same manner it can be de- ( 2 ) Prop , 6 ...
Page 89
... divided into fifteen parts , the arch CD , since it is the third part of the whole circum- ference , contains five of these parts , in like manner the arch CA contains three of them , therefore the arch AD contains two , and therefore ...
... divided into fifteen parts , the arch CD , since it is the third part of the whole circum- ference , contains five of these parts , in like manner the arch CA contains three of them , therefore the arch AD contains two , and therefore ...
Page 96
... divided into parts equal to x , and therefore r is a sub- multiple of AB . P. 1. B. 5 . Fig . 7 . PROP . VII . THEOR . If there be two magnitudes ( a and b ) equi - submultiples of two other magnitudes ( AC and BD ) , and there be taken ...
... divided into parts equal to x , and therefore r is a sub- multiple of AB . P. 1. B. 5 . Fig . 7 . PROP . VII . THEOR . If there be two magnitudes ( a and b ) equi - submultiples of two other magnitudes ( AC and BD ) , and there be taken ...
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.