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
Euclides T W Herbert. DUBLIN : GEORGE FOLds , printer , 1 , SAINT ANDrew - street , OPPOSITE TRINITY - STREET . ΤΟ The Right Reb . Edward Stanleg , D.D. ,
Euclides T W Herbert. DUBLIN : GEORGE FOLds , printer , 1 , SAINT ANDrew - street , OPPOSITE TRINITY - STREET . ΤΟ The Right Reb . Edward Stanleg , D.D. ,
Σελίδα 5
... opposite sides are parallel . 31. A square is a quadrilateral , which is equilateral and equiangular . 32. Rectilineal figures which have more than four sides , are called polygons . POSTULATES . 1. Let it be granted that a right line ...
... opposite sides are parallel . 31. A square is a quadrilateral , which is equilateral and equiangular . 32. Rectilineal figures which have more than four sides , are called polygons . POSTULATES . 1. Let it be granted that a right line ...
Σελίδα 8
... ) ; the bases ( EF and AC ) will be equal ; and the angles at the bases , opposite to equal sides , will be equal ( E to A and F to C ) and also the triangles themselves are equal . E D FA For if the triangles be so applied 8 FIRST BOOK ,
... ) ; the bases ( EF and AC ) will be equal ; and the angles at the bases , opposite to equal sides , will be equal ( E to A and F to C ) and also the triangles themselves are equal . E D FA For if the triangles be so applied 8 FIRST BOOK ,
Σελίδα 10
... opposite . PROPOSITION VI . THEOREM . If two angles ( B and C ) of a triangle ( BAC ) be equal , the sides opposite to them ( AC and AB ) are equal . If not , let one of them BA be made greater than the other , cut off a right line BD ...
... opposite . PROPOSITION VI . THEOREM . If two angles ( B and C ) of a triangle ( BAC ) be equal , the sides opposite to them ( AC and AB ) are equal . If not , let one of them BA be made greater than the other , cut off a right line BD ...
Σελίδα 12
... opposite to the equal sides are equal , and also the triangles themselves . PROPOSITION IX . PROBLEM . To cut a given rectilineal angle ( BAC ) into two equal parts . From A take the equals AD and AE ( by Prop . 3 , ) draw DE , and upon ...
... opposite to the equal sides are equal , and also the triangles themselves . PROPOSITION IX . PROBLEM . To cut a given rectilineal angle ( BAC ) into two equal parts . From A take the equals AD and AE ( by Prop . 3 , ) draw DE , and upon ...
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.