The geometry of the three first books of Euclid, by direct proof from definitions alone, by H. Wedgwood1856 |
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Αποτελέσματα 1 - 5 από τα 31.
Σελίδα 45
... ( Prop . 9 ) the angle CAB is equal to GCD . Next , let AB , CD , be straight lines in the same plane , making the angle CAB equal to GCD ; CD shall be parallel to A B. Because AC is in the same direction with CG , and the angle C A B is ...
... ( Prop . 9 ) the angle CAB is equal to GCD . Next , let AB , CD , be straight lines in the same plane , making the angle CAB equal to GCD ; CD shall be parallel to A B. Because AC is in the same direction with CG , and the angle C A B is ...
Σελίδα 49
... ( Prop . 14 ) . Let the triangles ABC , DEF ( Fig . 11 ) , have the angles BA C , B C A , equal to EDF , EF D , respectively , and therefore the third angle ABC equal to DE F , and let any side A C be equal to D DF . The remaining sides ...
... ( Prop . 14 ) . Let the triangles ABC , DEF ( Fig . 11 ) , have the angles BA C , B C A , equal to EDF , EF D , respectively , and therefore the third angle ABC equal to DE F , and let any side A C be equal to D DF . The remaining sides ...
Σελίδα 52
... ( Prop . 18 , Cor . ) ; that is , one of the two A B , A C , is greater than the other . But in a triangle having one side greater than another , the angle opposite the greater side is greater than the angle opposite the less ; and in the ...
... ( Prop . 18 , Cor . ) ; that is , one of the two A B , A C , is greater than the other . But in a triangle having one side greater than another , the angle opposite the greater side is greater than the angle opposite the less ; and in the ...
Σελίδα 55
... Prop . 16 , Cor . ) , the opposite angles BA C , EDF are unequal , or one of them is the greater of the two and ( by Prop . 24 ) the base PROPOSITIONS . 55.
... Prop . 16 , Cor . ) , the opposite angles BA C , EDF are unequal , or one of them is the greater of the two and ( by Prop . 24 ) the base PROPOSITIONS . 55.
Σελίδα 56
Euclides Hensleigh Wedgwood. two and ( by Prop . 24 ) the base opposite the greater angle is the greater . But in triangles A B C , DEF the base EF is greater than A C ; there- fore E F is opposite the greater of the two angles BAC , EDF ...
Euclides Hensleigh Wedgwood. two and ( by Prop . 24 ) the base opposite the greater angle is the greater . But in triangles A B C , DEF the base EF is greater than A C ; there- fore E F is opposite the greater of the two angles BAC , EDF ...
Άλλες εκδόσεις - Προβολή όλων
The Geometry of the Three First Books of Euclid, by Direct Proof from ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2012 |
The Geometry of the Three First Books of Euclid, by Direct Proof from ... Euclid,Hensleigh Wedgwood Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
The Geometry of the Three First Books of Euclid, by Direct Proof From ... Euclid,Hensleigh Wedgwood Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D angle A B C angle ABC angle B A C angle BAC AUGUSTUS DE MORGAN axiom of Euclid B C is equal base B C bisected centre Chap coincide conception cuts the circle D E F definition diameter DIONYSIUS LARDNER Electric Telegraph equal to twice ex absurdo exterior angle F. W. NEWMAN Fcap geometry Greek less London magnitude motion opposite angles parallel straight lines parallelogram perpendicular plane surface position price 5d Professor Prop proportion proposition rectangle A C rectangle A D rectangle contained relation right angles segment sides A B squares of A C straight line joining tion touching the circle track transverse triangle A B C twice the rectangle University College Vols wherefore wholly
Δημοφιλή αποσπάσματα
Σελίδα 62 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Σελίδα 64 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Σελίδα 98 - Museum of Science and Art. THE MUSEUM OF SCIENCE AND ART. Edited by DIONYSIUS LARDNER, DCL, formerly Professor of Natural Philosophy and Astronomy in University College, London. With upwards of 1 200 Engravings on Wood.
Σελίδα 80 - 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 25 - 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 78 - BAC is cut off from the given circle ABC containing an angle equal to the given angle D : Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other.
Σελίδα 97 - This is quite a novelty in chronological literature. It is an universal almanac — universal, that is, as respects time, past, present, and future. The main object of it is, as the compiler states, to supply the place of an old almanac, which is never at hand when wanted ; of the older almanac, which never was at hand ; and of the universal almanac in every shape IA more useful chronological handbook could scarcely be conceived.
Σελίδα 24 - 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.
Σελίδα 26 - If two triangles have two sides of the one equal to two sides of the...