The Elements of Euclid [book 1] for beginners, by J. Lowres1852 |
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Αποτελέσματα 1 - 5 από τα 9.
Σελίδα 13
... fall on DF , because the angles A and D are equal ( Hyp . ) ; and the point c must coincide with F , because the sides Ac and DF are equal ( Hyp . ) : and as the points B and c coincide with the points E and F , the lines BC and EF must ...
... fall on DF , because the angles A and D are equal ( Hyp . ) ; and the point c must coincide with F , because the sides Ac and DF are equal ( Hyp . ) : and as the points B and c coincide with the points E and F , the lines BC and EF must ...
Σελίδα 15
... falls on a side of the other B C. Then it is evident that the whole line BC is greater than its part BD ( Ax . 9. ) . Therefore in no case can the side BD be equal to BC . Which was to be demon- strated . C D A A B PROP . VIII . THEOR ...
... falls on a side of the other B C. Then it is evident that the whole line BC is greater than its part BD ( Ax . 9. ) . Therefore in no case can the side BD be equal to BC . Which was to be demon- strated . C D A A B PROP . VIII . THEOR ...
Σελίδα 16
... fall on E ( Prop . 7. ) , and the equal sides must coincide ( Ax . 10. ) ; therefore the angles в and E must also coincide , and are therefore equal ( Ax . 8. ) . And as the three sides of one triangle coincide with the three sides of ...
... fall on E ( Prop . 7. ) , and the equal sides must coincide ( Ax . 10. ) ; therefore the angles в and E must also coincide , and are therefore equal ( Ax . 8. ) . And as the three sides of one triangle coincide with the three sides of ...
Σελίδα 26
Euclides Jacob Lowres. PROP . XXVII . THEOR . If a right line fall upon two other right lines , and make the alternate angles equal to one another , the two lines are parallel . Let the line EF fall upon the two lines A B and C D , and ...
Euclides Jacob Lowres. PROP . XXVII . THEOR . If a right line fall upon two other right lines , and make the alternate angles equal to one another , the two lines are parallel . Let the line EF fall upon the two lines A B and C D , and ...
Σελίδα 27
... fall upon two parallel lines AB and CD ; then the alternate angles AGF and EHD are equal : and the exterior angle EGB equal to the interior angle EHD at the same side of E F and also the two interior angles BGF and EHD at the same side ...
... fall upon two parallel lines AB and CD ; then the alternate angles AGF and EHD are equal : and the exterior angle EGB equal to the interior angle EHD at the same side of E F and also the two interior angles BGF and EHD at the same side ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid [Book 1] for Beginners, by J. Lowres Joseph Butler,Thomas Codrington,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Elements of Euclid [book 1] for Beginners, by J. Lowres Joseph Butler,Thomas Codrington,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Elements of Euclid [book 1] for Beginners, by J. Lowres Joseph Butler,Thomas Codrington,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A B and C D A B C ABCD absurd alternate angles angle BAC angle equal angles ABC angles AGF applied base BC BC is equal bisect Book called centre circle coincide common Const Construction demonstrated describe diagonal divided double draw drawn equal Ax equal bases equal Hyp equal Prop equal sides equal to CD equilateral triangle exterior falls figure GEOMETRY given angle given line given point greater interior angles interior opposite angle join less Let the line lines A B manner meet parallel Prop parallelogram perpendicular PROB Problem produced proposition radii radius rectilineal figure remaining respectively equal right angles right angles Prop right line SCHOL Shilling side AB sides BC square standing Take THEOR theorem triangle ABC vertex W. W. D. PROP whole
Δημοφιλή αποσπάσματα
Σελίδα 10 - Things which are halves of the same are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Σελίδα 10 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.
Σελίδα 40 - 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 10 - 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...
Σελίδα 10 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 39 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Σελίδα 20 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 29 - 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 equal to two right angles.
Σελίδα 22 - Any two sides of a triangle are together greater than the third side.
Σελίδα 10 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal.