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

### From inside the book

Results 1-5 of 67

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**hypoth**. PROP . V. THEOR . In an isosceles triangle ( BAC ) the angles at the base ( ABC and ACB ) are equal to one another ; and if the equal sides be produced , the angles below the base ( FBC and GCB ) shall also be equal . Take any ... Page 7

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**hypoth**equal to the whole , which is absurd : therefore neither of the sides AB or AC is greater than the other ; they are therefore equal to one another . Cor . Hence every equiangular triangle is also equi- lateral ; for whatever side ... Page 8

Euclid. 116 I 19 c 20 Fig . 19 . ( 6 )

Euclid. 116 I 19 c 20 Fig . 19 . ( 6 )

**hypoth**. ( 7 ) prop 5 . ( 8 ) ax . 9 . Fig . 20 . Fig . 21 . See N. right line cannot have their conterminous sides equal , when the vertex of each of the triangles is without the other . Secondly ... Page 11

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**hypoth**. CBA and ABD taken together are equal to CBA and ABE , take away from these equal quantities CBA which is common to both , and ABE shall be equal to ABD , a part to the whole , which is absurd . There- fore BE is not the ... Page 16

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**hypoth**. Since the right lines AG and AC are equal ( 3 ) , the angles ACG and AGC are equal ( 4 ) ; but the angle ( 4 ) Prop.5 . BGC is greater than AGC , therefore greater than ACG , and therefore greater than BCG . Then in the ...### 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.