Euclid's Elements of Geometry |
From inside the book
Results 1-5 of 86
Page 2
... greater than a right angle , is called obtuse . 13. The angle ABD , which is less than a right angle , is called acute . A 8 D 14. A plane figure is a plane superficies , bounded on every side by one or more lines . 15. A circle is a ...
... greater than a right angle , is called obtuse . 13. The angle ABD , which is less than a right angle , is called acute . A 8 D 14. A plane figure is a plane superficies , bounded on every side by one or more lines . 15. A circle is a ...
Page 4
... greater than its part . 10. Two right lines cannot enclose a space : 11. All right angles are equal to one another . 12. If two right lines , meeting a right line , make the internal angles on the same side less than two right angles ...
... greater than its part . 10. Two right lines cannot enclose a space : 11. All right angles are equal to one another . 12. If two right lines , meeting a right line , make the internal angles on the same side less than two right angles ...
Page 6
... greater of two given right lines ( AB and CF ) to cut off a part equal to the less . From either extremity A of the greater right line , draw AD , equal o the less CF of the given lines ( by Prop . 2 ) . From the centre A , with the ...
... greater of two given right lines ( AB and CF ) to cut off a part equal to the less . From either extremity A of the greater right line , draw AD , equal o the less CF of the given lines ( by Prop . 2 ) . From the centre A , with the ...
Page 8
... greater than the other , cut off a right line BD equal to AC ( by Prop . 3 ) , and draw CD . Since , in the triangles DBC , ACB , the sides DB , BC , are equal to the sides AC , CB , and the angles DBC and ACB , which are contained by ...
... greater than the other , cut off a right line BD equal to AC ( by Prop . 3 ) , and draw CD . Since , in the triangles DBC , ACB , the sides DB , BC , are equal to the sides AC , CB , and the angles DBC and ACB , which are contained by ...
Page 9
... greater than BCD ; but BDC is greater than ADC ( by Ax . 9 ) , and therefore- -BDC is greater than BCD : but in the triangle CBD , the sides BC and BD are equal ( by Hypoth . ) , therefore . the angles BDC and BCD are equal ( by Prop ...
... greater than BCD ; but BDC is greater than ADC ( by Ax . 9 ) , and therefore- -BDC is greater than BCD : but in the triangle CBD , the sides BC and BD are equal ( by Hypoth . ) , therefore . the angles BDC and BCD are equal ( by Prop ...
Other editions - View all
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington No preview available - 2018 |
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington No preview available - 2022 |
Euclid's Elements of Geometry: Translated from the Latin of ... Thomas ... Thomas Elrington No preview available - 2015 |
Common terms and phrases
absurd AC and CB AC by Prop AC is equal angle ABC angles by Prop arch base bisected centre circumference CKMB co-efficient Const contained in CD contained oftener divided divisor double draw drawn equal angles equal by Constr equal by Hypoth equal by Prop equal to twice equation equi equi-multiples equi-submultiples equiangular equilateral external angle fore four magnitudes proportional given angle given circle given line given right line given triangle gonal half a right inscribed less multiplying oftener contained parallel parallelogram perpendicular PROPOSITION quantities rectangle under AC rectilineal figure remaining angles remaining side right angles right line AC Schol segment side AC similar similarly demonstrated squares of AC submultiple subtract THEOREM tiple touches the circle triangle BAC twice the rectangle
Popular passages
Page 18 - If two triangles have two sides of the one equal to two sides of the...
Page 28 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Page 207 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 216 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 127 - In any proportion, the product of the means is equal to the product of the extremes.
Page 161 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
Page 112 - To reduce fractions of different denominators to equivalent fractions having a common denominator. RULE.! Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 213 - ... are to one another in the duplicate ratio of their homologous sides.
Page 163 - Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.
Page 88 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.