The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner CorrectedDesilver, 1829 - 516 σελίδες |
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Αποτελέσματα 1 - 5 από τα 99.
Σελίδα 14
... less . Let AB and C be the two giv- en straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and ...
... less . Let AB and C be the two giv- en straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and ...
Σελίδα 25
... less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII . THEOR . THE greater side of ... less than it ; it is not equal , because then the angle ABC would be equal ( 5. 1. ) to the an- gle ACB ; but it is not ...
... less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII . THEOR . THE greater side of ... less than it ; it is not equal , because then the angle ABC would be equal ( 5. 1. ) to the an- gle ACB ; but it is not ...
Σελίδα 26
... less than the other two sides of the triangle , but shall contain a greater angle . * Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less ...
... less than the other two sides of the triangle , but shall contain a greater angle . * Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less ...
Σελίδα 30
... less ; because then the base BC would be less ( 24. 1. ) than the base EF ; but it is not ; therefore the angle BAC is not less AA B C E F than the angle EDF ; and it was shown that it is not equal to it ; therefore the angle BAC is ...
... less ; because then the base BC would be less ( 24. 1. ) than the base EF ; but it is not ; therefore the angle BAC is not less AA B C E F than the angle EDF ; and it was shown that it is not equal to it ; therefore the angle BAC is ...
Σελίδα 33
... less than two right angles ; but those straight lines which , with another straight line falling upon them , make the interior angles on the same side less than two right angles , do meet ( 12. ax . ) * together if continually pro ...
... less than two right angles ; but those straight lines which , with another straight line falling upon them , make the interior angles on the same side less than two right angles , do meet ( 12. ax . ) * together if continually pro ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 81 - The angles in the same segment of a circle are equal to one another.
Σελίδα 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 33 - 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.
Σελίδα 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 96 - 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.
Σελίδα 155 - 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.
Σελίδα 22 - ANY two angles of a triangle are together less than two right angles.
Σελίδα 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Σελίδα 24 - Any two sides of a triangle are together greater than the third side.