The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 sider |
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Side 23
... Q.E. D. PROP . XXVII . THEOR . If a straight line falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines shall be parallel . Let the straight line EF , which falls upon the two ...
... Q.E. D. PROP . XXVII . THEOR . If a straight line falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines shall be parallel . Let the straight line EF , which falls upon the two ...
Side 24
... Q.E. D. PROP . XXVIII . THEOR . If a straight line falling upon two other straight lines makes the exterior angle equal to the interior and opposite upon the same side of the line ; or makes the interior angles upon the same side ...
... Q.E. D. PROP . XXVIII . THEOR . If a straight line falling upon two other straight lines makes the exterior angle equal to the interior and opposite upon the same side of the line ; or makes the interior angles upon the same side ...
Side 25
... Q.E.D. PROP . XXX . THEOR . Straight lines which are parallel to the same straight line parallel to one another . Let AB , CD be each of them parallel to EF ; AB is also parallel to CD . C B H F -D Let the straight line GHK cut BOOK . I ...
... Q.E.D. PROP . XXX . THEOR . Straight lines which are parallel to the same straight line parallel to one another . Let AB , CD be each of them parallel to EF ; AB is also parallel to CD . C B H F -D Let the straight line GHK cut BOOK . I ...
Side 26
... Q.E.D. PROP . XXXI . PROB . To draw a straight line through a given point parallel to a given straight line . Let A be the given point , and BC the given straight line ; it is required to draw a straight line through the point a ...
... Q.E.D. PROP . XXXI . PROB . To draw a straight line through a given point parallel to a given straight line . Let A be the given point , and BC the given straight line ; it is required to draw a straight line through the point a ...
Side 27
... Q.E. D. COR . 1. All the interior angles of any rec- tilineal figure , together with four right angles , are equal ... PROP . XXXII . 27.
... Q.E. D. COR . 1. All the interior angles of any rec- tilineal figure , together with four right angles , are equal ... PROP . XXXII . 27.
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Vanlige uttrykk og setninger
ABCD adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle CAB angle EDF angle equal angles CBA base BC BC is equal bisect centre circle ABC circumference diameter divided double draw a straight equal angles equal circles equal straight lines equal to FB exterior angle fore given point given rectilineal angle given straight line gnomon greater half a right hypotenuse isosceles triangle less Let ABC Let the straight line be drawn opposite angles parallel parallelogram perpendicular PROB produced Q. E. D. PROP rectangle AE rectangle contained rectilineal figure remaining angle right angles segment semicircle side BC square of AC straight line AB straight line AC straight line drawn THEOR touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle
Populære avsnitt
Side 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 20 - If two triangles have two sides of the one equal to two sides of the...
Side 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Side 17 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.
Side 84 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets it shall touch the circle.
Side 82 - If from any point without a circle two straight lines be drawn, one of -which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 11 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Side 19 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i.
Side 7 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.