The Elements of Euclid [book 1] for beginners, by J. Lowres1852 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 8.
Σελίδα 6
... the one advanced would lead to an absurdity or impossibility . The sentence which expresses the substance of a proposition is called the Enunciation . DEFINITIONS . 1. A point is that which has no EXPLANATIONS OF TERMS. ...
... the one advanced would lead to an absurdity or impossibility . The sentence which expresses the substance of a proposition is called the Enunciation . DEFINITIONS . 1. A point is that which has no EXPLANATIONS OF TERMS. ...
Σελίδα 14
... ; a part equal to the whole , which is absurd ; therefore neither of the sides CA and CB is greater than the other : they are therefore equal . Which was to be demonstrated . PROP . VII . THEOR . If two triangles , 14 PROP . V. VI .
... ; a part equal to the whole , which is absurd ; therefore neither of the sides CA and CB is greater than the other : they are therefore equal . Which was to be demonstrated . PROP . VII . THEOR . If two triangles , 14 PROP . V. VI .
Σελίδα 15
... absurd ; therefore the sides BC and BD are not equal . CASE 2. When the vertex D of one triangle is within the other . E Produce the sides AC and AD to E and F : then in the triangle AC D , be- cause the sides AC and AD are equal ( Hyp ...
... absurd ; therefore the sides BC and BD are not equal . CASE 2. When the vertex D of one triangle is within the other . E Produce the sides AC and AD to E and F : then in the triangle AC D , be- cause the sides AC and AD are equal ( Hyp ...
Σελίδα 19
... absurd ; therefore BE does not form a right line with AB ; and in the same manner it can be proved that no other line but BC can form a right line with AB : therefore A B and BC form one continued right line . W. W. D. PROP . XV . THEOR ...
... absurd ; therefore BE does not form a right line with AB ; and in the same manner it can be proved that no other line but BC can form a right line with AB : therefore A B and BC form one continued right line . W. W. D. PROP . XV . THEOR ...
Σελίδα 25
... absurd ; therefore A B and DE are not unequal , therefore they are equal ; and also A c is equal to DF , and the angles at A and D are equal ( Hyp . ) ; therefore B C is equal to E F , the angle в to the angle E , and the triangles ...
... absurd ; therefore A B and DE are not unequal , therefore they are equal ; and also A c is equal to DF , and the angles at A and D are equal ( Hyp . ) ; therefore B C is equal to E F , the angle в to the angle E , and the triangles ...
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.