The Elements of Euclid [book 1] for beginners, by J. Lowres1852 |
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Αποτελέσματα 6 - 10 από τα 14.
Σελίδα 18
... produced in the points E and F ; bisect EF in the point & ( Prop . 10. ) , and join ca ; then the line CG is perpen- dicular to A B. For draw the lines CE and CF ; then in the triangles GEC and GFC , the side CE is equal to CF , being ...
... produced in the points E and F ; bisect EF in the point & ( Prop . 10. ) , and join ca ; then the line CG is perpen- dicular to A B. For draw the lines CE and CF ; then in the triangles GEC and GFC , the side CE is equal to CF , being ...
Σελίδα 20
... produced , the exterior angle is greater than either of the interior opposite angles . Let the side AB of the triangle ABC be produced to D ; the exterior angle CBD is greater than either of the interior opposite angles CAB or ACB ...
... produced , the exterior angle is greater than either of the interior opposite angles . Let the side AB of the triangle ABC be produced to D ; the exterior angle CBD is greater than either of the interior opposite angles CAB or ACB ...
Σελίδα 22
... Produce AD to E ; then in the triangle ABE , the sides AB and BE are greater than the third side AE ( Prop . 20. ) ; add EC to each , then AB and BC are greater than AE and EC ; but in the triangle CED , the sides DE and EC are greater ...
... Produce AD to E ; then in the triangle ABE , the sides AB and BE are greater than the third side AE ( Prop . 20. ) ; add EC to each , then AB and BC are greater than AE and EC ; but in the triangle CED , the sides DE and EC are greater ...
Σελίδα 26
... produced . Suppose them to meet in L ; then GHL is triangle , and the exterior angle A G H is greater than the interior angle EHD ( Prop . 16. ) ; but these angles are also equal ( Hyp . ) , which is absurd ; therefore A B and C D do ...
... produced . Suppose them to meet in L ; then GHL is triangle , and the exterior angle A G H is greater than the interior angle EHD ( Prop . 16. ) ; but these angles are also equal ( Hyp . ) , which is absurd ; therefore A B and C D do ...
Σελίδα 27
... produced , would meet at the side BD ( Ax . 12. ) : but they are parallel , and therefore cannot meet ( Def . 30. ) , which is absurd ; therefore neither of the angles AG F and EHD is greater than the other , therefore they are equal ...
... produced , would meet at the side BD ( Ax . 12. ) : but they are parallel , and therefore cannot meet ( Def . 30. ) , which is absurd ; therefore neither of the angles AG F and EHD is greater than the other , therefore they are equal ...
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 is equal ABC and ABD ABCD adjacent angles alternate angles angle ABC angle BAC angle equal angle opposite angles AGF angles CAB angles DBA base BC BC is equal BD Prop BGF and EHD bisect coincide DBC are equal demonstrated describe an equilateral diagonal draw EHD are equal equal Ax equal bases equal Hyp equal Prop equal sides equal to CD equal triangles equilateral triangle EUCLID's ELEMENTS exterior given angle given line given point greater than AC hypotenuse interior angles interior opposite angle isosceles triangle join Let the line line BC lines A B parallel Prop parallel to BC parallelogram perpendicular price One Shilling PROB produced proposition rectilineal figure respectively equal right angles Prop SCHOL side A B sides AB sides BC THEOR triangle ABC triangles are equal Twickenham vertex W. W. D. PROP
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.