The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and ExercisesMacmillan, 1867 - 400 sider |
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Resultat 1-5 av 59
Side 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 ...
Side 50
... squares described on the sides BA , AC . On BC describe the square BDEC , and on BA , AC de- scribe the squares GB , HC ; [ I. 46 . through A draw AL parallel to BD or CE ; [ I. 31 . and join AD , FC . Then , because the angle BAC is a ...
... squares described on the sides BA , AC . On BC describe the square BDEC , and on BA , AC de- scribe the squares GB , HC ; [ I. 46 . through A draw AL parallel to BD or CE ; [ I. 31 . and join AD , FC . Then , because the angle BAC is a ...
Side 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 ...
Side 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 ...
Side 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 ...
Andre utgaver - Vis alle
The Elements of Euclid for the Use of Schools and Colleges Isaac Todhunter Uten tilgangsbegrensning - 1872 |
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1884 |
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1883 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 286 - 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 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 34 - 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...
Side 37 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Side 12 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Side 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Side 220 - If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 354 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.
Side 104 - 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 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.