Euclid's Elements of geometry, the first three books (the fourth, fifth, and sixth books) tr. from the Lat. To which is added, A compendium of algebra (A compendium of trigonometry).1846 |
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Seite 3
... extremities of a line are points . 4. A right line , is that which lies evenly between its extremities . 5. A superficies , is that which has only A length and breadth . 6. The boundings of a superficies are lines . 8 7. A plane ...
... extremities of a line are points . 4. A right line , is that which lies evenly between its extremities . 5. A superficies , is that which has only A length and breadth . 6. The boundings of a superficies are lines . 8 7. A plane ...
Seite 4
... extremities terminate in the circumference . 18. A radius is a right line drawn from the centre to the circumference . 19. A semicircle , is the figure which is contained by the diameter and the part of the circumference which the ...
... extremities terminate in the circumference . 18. A radius is a right line drawn from the centre to the circumference . 19. A semicircle , is the figure which is contained by the diameter and the part of the circumference which the ...
Seite 7
... extremities of the given right line AB . ( by Post . 1 ) . It is manifest that ABC is a triangle , constructed upon the ... extremity B of the given right line ( by Post . 1 ) ; upon AB construct an equilateral triangle ADB ( by Prop . 1 ) ...
... extremities of the given right line AB . ( by Post . 1 ) . It is manifest that ABC is a triangle , constructed upon the ... extremity B of the given right line ( by Post . 1 ) ; upon AB construct an equilateral triangle ADB ( by Prop . 1 ) ...
Seite 8
... extremity of the given line , to which the right line from the given point is drawn , and also according to the different side of that line on which the triangle is constructed . PROPOSITION III . PROBLEM . From the greater of two given ...
... extremity of the given line , to which the right line from the given point is drawn , and also according to the different side of that line on which the triangle is constructed . PROPOSITION III . PROBLEM . From the greater of two given ...
Seite 13
... extremities of a given right line , if the right line be first produced . PROPOSITION XII . PROBLEM . From a given point ( C ) without a given indefinite right line ( AB ) to draw a perpendicular to it . From the centre C describe a ...
... extremities of a given right line , if the right line be first produced . PROPOSITION XII . PROBLEM . From a given point ( C ) without a given indefinite right line ( AB ) to draw a perpendicular to it . From the centre C describe a ...
Häufige Begriffe und Wortgruppen
absurd AC and CB AC by Prop AC is equal angle ABC angle equal angles by Prop arch bisected centre circumference co-efficient Const construct contained oftener diameter divided divisor double equal angles equal by Constr equal by Hypoth equal by Prop equal right lines equal to AC equal to twice equi-multiples equi-submultiples equiangular equilateral external angle fore fraction given angle given circle given line given right line given triangle greater half a right inscribed less multiplied opposite parallel parallelogram perpendicular PROPOSITION quantities quotient ratio rectangle under AC remaining angles remaining side right angle right line AB right line AC SCHOL segment semicircle side AC similar similarly demonstrated squares of AC submultiple subtract THEOREM tiple touches the circle triangle BAC twice the rectangle twice the square whole
Beliebte Passagen
Seite 20 - If two triangles have two sides of the one equal to two sides of the...
Seite 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Seite 209 - ... 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.
Seite 218 - 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.
Seite 114 - 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.
Seite 90 - 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.
Seite 129 - In any proportion, the product of the means is equal to the product of the extremes.
Seite 163 - 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.
Seite 215 - ... are to one another in the duplicate ratio of their homologous sides.
Seite 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.