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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Σελίδα
... circle . With paying attention , and not stepping forward too quickly , until all going before is established in the mind , students will advance with pleasure and stability , finding that getting an idea of the utility of Algebra , at ...
... circle . With paying attention , and not stepping forward too quickly , until all going before is established in the mind , students will advance with pleasure and stability , finding that getting an idea of the utility of Algebra , at ...
Σελίδα 4
... circle is a plane figure , contained by one line , which is called the circum- ference ; to which from a certain point within the figure , all right lines drawn are equal . 16. That point is called the centre of the circle . 17. A ...
... circle is a plane figure , contained by one line , which is called the circum- ference ; to which from a certain point within the figure , all right lines drawn are equal . 16. That point is called the centre of the circle . 17. A ...
Σελίδα 5
... circle can be described from any centre , with any radius . COMMON NOTIONS , OR AXIOMS . 1. Things which are equal to the same are equal to one another . 2. If equals be added to equals , the wholes will be equal . 3. If from equals ...
... circle can be described from any centre , with any radius . COMMON NOTIONS , OR AXIOMS . 1. Things which are equal to the same are equal to one another . 2. If equals be added to equals , the wholes will be equal . 3. If from equals ...
Σελίδα 7
... circle BCD , ( by Post . 3 ) . From the centre B and with the interval BA , describe the circle ACE . From the intersection C , draw the right lines CA , and CB , to the extremities of the given right line AB . ( by Post . 1 ) . It is ...
... circle BCD , ( by Post . 3 ) . From the centre B and with the interval BA , describe the circle ACE . From the intersection C , draw the right lines CA , and CB , to the extremities of the given right line AB . ( by Post . 1 ) . It is ...
Σελίδα 8
... circle GLO ( by Def . 15 ) ; take away both DA and DB , which are also equal ( by Const . ) and the remainder AL will be equal to the remainder BG ( by Ax . 3 ) ; but BG is equal to BC , because they are the radii of the same circle GCF ...
... circle GLO ( by Def . 15 ) ; take away both DA and DB , which are also equal ( by Const . ) and the remainder AL will be equal to the remainder BG ( by Ax . 3 ) ; but BG is equal to BC , because they are the radii of the same circle GCF ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 20 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 129 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 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.
Σελίδα 215 - ... are to one another in the duplicate ratio of their homologous sides.
Σελίδα 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.