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 |
Inni boken
Resultat 1-5 av 26
Side 5
... parallelogram , is a quadrilateral figure , whose 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 ...
... parallelogram , is a quadrilateral figure , whose 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 ...
Side 28
... parallelogram if one angle be right , the remaining angles will be right angles . For the adjacent angle is right , because with a right angle it is equal to two right angles , ( by Prop . 29 ) ; and the opposite angles are right ...
... parallelogram if one angle be right , the remaining angles will be right angles . For the adjacent angle is right , because with a right angle it is equal to two right angles , ( by Prop . 29 ) ; and the opposite angles are right ...
Side 29
... parallelogram BF ; and subtract the triangle CFD from the same quadrilateral , the remainder is the parallelogram BD ; therefore the parallelograms BD and BF are equal ( by Ax . 3. ) PROPOSITION XXXVI , THEOREM . Parallelograms ( BD and ...
... parallelogram BF ; and subtract the triangle CFD from the same quadrilateral , the remainder is the parallelogram BD ; therefore the parallelograms BD and BF are equal ( by Ax . 3. ) PROPOSITION XXXVI , THEOREM . Parallelograms ( BD and ...
Side 30
Euclides T W Herbert. Prop . 33 ) , and BG is a parallelogram , therefore it is equal to both BD and EG ( by Prop . 35 ) , and therefore BD and EG are equal to one another . ( by Ax . 1. ) PROPOSITION XXXVII . THEOREM . Triangles ( BAC ...
Euclides T W Herbert. Prop . 33 ) , and BG is a parallelogram , therefore it is equal to both BD and EG ( by Prop . 35 ) , and therefore BD and EG are equal to one another . ( by Ax . 1. ) PROPOSITION XXXVII . THEOREM . Triangles ( BAC ...
Side 31
... parallelogram ( BF ) and a triangle ( BAC ) have the same base , and be between the same parallels , it will be double of the triangle . For draw CD . The triangle BDC is equal to to the triangle BAC ( by Prop . 37 , ) but BE is double ...
... parallelogram ( BF ) and a triangle ( BAC ) have the same base , and be between the same parallels , it will be double of the triangle . For draw CD . The triangle BDC is equal to to the triangle BAC ( by Prop . 37 , ) but BE is double ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 20 - If two triangles have two sides of the one equal to two sides of the...
Side 30 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 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.
Side 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.
Side 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.
Side 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.
Side 129 - In any proportion, the product of the means is equal to the product of the extremes.
Side 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.
Side 215 - ... are to one another in the duplicate ratio of their homologous sides.
Side 160 - PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle.