Euclid's Elements [book 1-6] with corrections, by J.R. Young1838 |
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Página 42
... parallelogram are equal to one another , and the diameter bisects it , that is , divides it into two equal parts . N. B .-- A parallelogram is a four - sided figure , of which the oppo- site sides are parallel : and the diameter is the ...
... parallelogram are equal to one another , and the diameter bisects it , that is , divides it into two equal parts . N. B .-- A parallelogram is a four - sided figure , of which the oppo- site sides are parallel : and the diameter is the ...
Página 43
... parallelogram ACDB into two equal parts . Q. E. D. PROP . XXXV . THEOR . Parallelograms upon the same base , and between the same parallels , are equal to one another . Let the parallelograms ABCD , EBCF be upon the same base BC , and ...
... parallelogram ACDB into two equal parts . Q. E. D. PROP . XXXV . THEOR . Parallelograms upon the same base , and between the same parallels , are equal to one another . Let the parallelograms ABCD , EBCF be upon the same base BC , and ...
Página 44
... parallelogram ABCD is equal to the parallelogram EBCF . Therefore parallel- ograms upon the same base , & c . Q. E. v . * 4 . 1 . * 3 Ax . PROP . XXXVI . THEOR . Parallelograms upon equal bases , and between the same parallels , are ...
... parallelogram ABCD is equal to the parallelogram EBCF . Therefore parallel- ograms upon the same base , & c . Q. E. v . * 4 . 1 . * 3 Ax . PROP . XXXVI . THEOR . Parallelograms upon equal bases , and between the same parallels , are ...
Página 45
... parallelogram EFGH is equal to the same * Def . 34. 1 . +1 Ax . EBCH : therefore the parallelogram ABCD is equalt to EFGH . Wherefore parallelograms , & c . Q. E. D. PROP . XXXVII . THEOR . Triangles upon the same base , and between the ...
... parallelogram EFGH is equal to the same * Def . 34. 1 . +1 Ax . EBCH : therefore the parallelogram ABCD is equalt to EFGH . Wherefore parallelograms , & c . Q. E. D. PROP . XXXVII . THEOR . Triangles upon the same base , and between the ...
Página 46
... parallelogram GBCA , because the diameter AB bisects * it ; and the triangle DEF is the half of the parallelogram DEFH , because the diameter DF bisects it : but the halves of equal things are equal : therefore the triangle ABC is equal ...
... parallelogram GBCA , because the diameter AB bisects * it ; and the triangle DEF is the half of the parallelogram DEFH , because the diameter DF bisects it : but the halves of equal things are equal : therefore the triangle ABC is equal ...
Otras ediciones - Ver todas
Euclid's Elements [Book 1-6] With Corrections, by J.R. Young Euclides Sin vista previa disponible - 2023 |
Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Sin vista previa disponible - 2018 |
Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angles equal antecedent arc BC base BC BC is equal bisected centre circle ABC circumference consequent Const demonstrated described diameter double draw equal angles equal to AC equiangular equilateral and equiangular equimultiples Euclid exterior angle fore Geometry given circle given straight line gnomon greater inscribed join less Let ABC Let the straight logarithm multiple opposite angle parallel parallelogram pentagon perpendicular PROB proportion proposition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle segment side BC similar sine square of AC straight line AB straight line AC tangent THEOR touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Pasajes populares
Página 30 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Página 105 - 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.
Página 50 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 61 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Página 65 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Página 70 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Página 41 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 172 - 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.
Página 45 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Página 38 - If a, straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles.