The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth BooksMacmillan, 1886 - 400 Seiten |
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Seite 49
... square on a given straight line . Let AB be the given straight line : it is required to describe a square on AB . From the point A draw AC at right angles to AB ; [ I. 11 . and make AD equal to AB ; [ I. 3 . through D draw DE parallel ...
... square on a given straight line . Let AB be the given straight line : it is required to describe a square on AB . From the point A draw AC at right angles to AB ; [ I. 11 . and make AD equal to AB ; [ I. 3 . through D draw DE parallel ...
Seite 50
... squares described on the sides BA , AC . On BC describe the square BDEC , and on BA , AC de- scribe the squares GB , HC ; H [ I. 46 . F through A draw AL parallel to BD or CE ; [ I. 31 . and join AD , FC . Then , because the angle BAC ...
... squares described on the sides BA , AC . On BC describe the square BDEC , and on BA , AC de- scribe the squares GB , HC ; H [ I. 46 . F through A draw AL parallel to BD or CE ; [ I. 31 . and join AD , FC . Then , because the angle BAC ...
Seite 51
... square GB is double of the triangle FBC , because they are on the same base FB , and between the same parallels FB ... AC . Therefore the square described on the side BC is equal to the squares described on the sides BA , AC . Wherefore ...
... square GB is double of the triangle FBC , because they are on the same base FB , and between the same parallels FB ... AC . Therefore the square described on the side BC is equal to the squares described on the sides BA , AC . Wherefore ...
Seite 52
... square on DC is equal to the squares on DA , AC . [ I. 47 . And , by hypothesis , the square on BC is equal to the squares on BA , AC . Therefore the square on DC'is equal to the square on BC . [ Ax.1 . Therefore also the side DC is ...
... square on DC is equal to the squares on DA , AC . [ I. 47 . And , by hypothesis , the square on BC is equal to the squares on BA , AC . Therefore the square on DC'is equal to the square on BC . [ Ax.1 . Therefore also the side DC is ...
Seite 54
... AC , shall be equal to the square on AB . [ Note . To avoid repeating the word contained too frequently , the rectangle contained by two straight lines AB , AC is sometimes simply called the rectangle AB , AC . ] On AB describe the ...
... AC , shall be equal to the square on AB . [ Note . To avoid repeating the word contained too frequently , the rectangle contained by two straight lines AB , AC is sometimes simply called the rectangle AB , AC . ] On AB describe the ...
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Häufige Begriffe und Wortgruppen
ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore