A Text-book of Euclid's Elements for the Use of Schools, Βιβλίο 1Macmillan, 1904 - 456 σελίδες |
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Σελίδα xii
... THEOREMS AND EXAMPLES ON BOOK II . 158 BOOK III . DEFINITIONS , ETC. PROPOSITIONS 1-37 NOTE ON THE METHOD OF LIMITS AS APPLIED TO TANGENCY Theorems and Examples on Book III . 163 167 231 I. ON THE CENTRE AND CHORDS OF A CIRCLE 233 II ...
... THEOREMS AND EXAMPLES ON BOOK II . 158 BOOK III . DEFINITIONS , ETC. PROPOSITIONS 1-37 NOTE ON THE METHOD OF LIMITS AS APPLIED TO TANGENCY Theorems and Examples on Book III . 163 167 231 I. ON THE CENTRE AND CHORDS OF A CIRCLE 233 II ...
Σελίδα xii
... THEOREMS AND EXAMPLES ON BOOK II . 130 158 BOOK III . DEFINITIONS , ETC. PROPOSITIONS 1-37 163 167 NOTE ON THE METHOD OF LIMITS AS APPLIED TO TANGENCY 231 Theorems and Examples on Book III . I. ON THE CENTRE AND CHORDS OF A CIRCLE 233 ...
... THEOREMS AND EXAMPLES ON BOOK II . 130 158 BOOK III . DEFINITIONS , ETC. PROPOSITIONS 1-37 163 167 NOTE ON THE METHOD OF LIMITS AS APPLIED TO TANGENCY 231 Theorems and Examples on Book III . I. ON THE CENTRE AND CHORDS OF A CIRCLE 233 ...
Σελίδα 10
... Theorem proposes to prove the truth of some geometrical statement . 4. A Proposition consists of the following parts ... theorem . ( iv ) The Proof shews that the object proposed in a problem has been accomplished , or that the property ...
... Theorem proposes to prove the truth of some geometrical statement . 4. A Proposition consists of the following parts ... theorem . ( iv ) The Proof shews that the object proposed in a problem has been accomplished , or that the property ...
Σελίδα 21
... theorem , we enunciate a new theorem which is called the converse of the first . For example , in Prop . 5 it is assumed that AB = AC ; it is required to prove that the angle ABC = the angle ACB . Now in Prop . 6 it is assumed that the ...
... theorem , we enunciate a new theorem which is called the converse of the first . For example , in Prop . 5 it is assumed that AB = AC ; it is required to prove that the angle ABC = the angle ACB . Now in Prop . 6 it is assumed that the ...
Σελίδα 27
... theorems said to be converse to one another . Give an example . 5. Shew by an example that the converse of a true theorem is not itself necessarily true . 6. What is a corollary ? Quote the corollary to Proposition 5 ; and shew how its ...
... theorems said to be converse to one another . Give an example . 5. Shew by an example that the converse of a true theorem is not itself necessarily true . 6. What is a corollary ? Quote the corollary to Proposition 5 ; and shew how its ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal adjacent angles Algebra angle BAC angle equal base BC bisected bisectors centre chord circumference circumscribed circle concyclic Constr Describe a circle diagonal diameter divided equal angles equiangular Euclid Euclid's exterior angle find the locus given circle given point given straight line given triangle greater Hence hypotenuse inscribed circle isosceles triangle Let ABC line which joins magnitudes meet middle point nine-points circle opposite sides orthocentre par¹ parallelogram parm pass pedal triangle perp perpendiculars drawn plane XY polygon produced Proof proportional PROPOSITION PROPOSITION 13 prove quadrilateral radical axis radius rectangle contained rectilineal figure regular polygon right angles segment shew shewn side BC Similarly square straight line drawn tangent THEOREM triangle ABC twice the rect vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 353 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Σελίδα 340 - 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 65 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 162 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Σελίδα 326 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Σελίδα 162 - 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...
Σελίδα 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Σελίδα 79 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Σελίδα 18 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Σελίδα 242 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent ; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.