Euclid's Elements [book 1-6] with corrections, by J.R. Young1838 |
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Página 20
... segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B drawt BE at right angles to AB ; and because ABC is a straight line , the angle +11 . 1 . * 8 Def . CBE is ...
... segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B drawt BE at right angles to AB ; and because ABC is a straight line , the angle +11 . 1 . * 8 Def . CBE is ...
Página 76
... segment of a circle is the figure contained by an arc of a circle and the straight line joining its extremities ; which straight line is called the chord of the arc , or the base of the segment . VII . An angle in a segment is the angle ...
... segment of a circle is the figure contained by an arc of a circle and the straight line joining its extremities ; which straight line is called the chord of the arc , or the base of the segment . VII . An angle in a segment is the angle ...
Página 96
... segment of a circle are equal to one another . Let ABCD be a circle , and BAD , BED angles in the same segment BAED ; these angles shall be equal to one another . # 1 . 3 . Take F the centre of 96 YOUNG'S ELEMENTS OF EUCLID ,
... segment of a circle are equal to one another . Let ABCD be a circle , and BAD , BED angles in the same segment BAED ; these angles shall be equal to one another . # 1 . 3 . Take F the centre of 96 YOUNG'S ELEMENTS OF EUCLID ,
Página 97
... segment , & c . Q. E. D. # 1 Ax . PROP . XXII . THEOR . The opposite angles of any quadrilateral figure inscribed in ... segment CDAB ; and the angle ACB is equal to the angle ADB , because they are in the same segment ADCB : therefore ...
... segment , & c . Q. E. D. # 1 Ax . PROP . XXII . THEOR . The opposite angles of any quadrilateral figure inscribed in ... segment CDAB ; and the angle ACB is equal to the angle ADB , because they are in the same segment ADCB : therefore ...
Página 98
... segments must fall within the other : let ACB fall within ADB : draw the straight line BCD , and join CA , DA . And because the segment ACB is similart to the segment ADB , and that similar segments of circles * 10 Def . 3. contain ...
... segments must fall within the other : let ACB fall within ADB : draw the straight line BCD , and join CA , DA . And because the segment ACB is similart to the segment ADB , and that similar segments of circles * 10 Def . 3. contain ...
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.