A Text-book of Euclid's Elements: For the Use of Schools : Parts I and II, Containing Books I-VI, Βιβλία 1-6Macmillan, 1889 - 382 σελίδες |
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Σελίδα 5
... hypotenuse . 23. An obtuse - angled triangle is a triangle which has an obtuse angle . 24 . An acute - angled triangle is a triangle which has three acute angles . [ It will be seen hereafter ( Book I. Proposition 17 ) that every ...
... hypotenuse . 23. An obtuse - angled triangle is a triangle which has an obtuse angle . 24 . An acute - angled triangle is a triangle which has three acute angles . [ It will be seen hereafter ( Book I. Proposition 17 ) that every ...
Σελίδα 37
... greater than the interior opposite angle BAE , that is , than the angle BAC ; I. 16 . still more then is the angle BDC greater than the angle BAC . Q.E.D. EXERCISES ON PROPOSITIONS 18 AND 19 . 1. The hypotenuse BOOK I. 37 PROP . 21 .
... greater than the interior opposite angle BAE , that is , than the angle BAC ; I. 16 . still more then is the angle BDC greater than the angle BAC . Q.E.D. EXERCISES ON PROPOSITIONS 18 AND 19 . 1. The hypotenuse BOOK I. 37 PROP . 21 .
Σελίδα 38
... hypotenuse is the greatest side of a right - angled triangle . 2. If two angles of a triangle are equal to one another , the sides also , which subtend the equal angles , are equal to one another . Prop . 6 . Prove this indirectly by ...
... hypotenuse is the greatest side of a right - angled triangle . 2. If two angles of a triangle are equal to one another , the sides also , which subtend the equal angles , are equal to one another . Prop . 6 . Prove this indirectly by ...
Σελίδα 59
... hypotenuse . Hence the joining line is equal to half the hypotenuse . 5. Draw a straight line at right angles to a given finite straight line from one of its extremities , without producing the given straight line . [ Let AB be the ...
... hypotenuse . Hence the joining line is equal to half the hypotenuse . 5. Draw a straight line at right angles to a given finite straight line from one of its extremities , without producing the given straight line . [ Let AB be the ...
Σελίδα 82
... hypotenuse is equal to the sum of the squares described on the other two sides . H K B Let ABC be a right - angled triangle , having the angle BAC a right angle : then shall the square described on the hypotenuse BC be equal to the sum ...
... hypotenuse is equal to the sum of the squares described on the other two sides . H K B Let ABC be a right - angled triangle , having the angle BAC a right angle : then shall the square described on the hypotenuse BC be equal to the sum ...
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ABCD AC is equal adjacent angles angle BAC angle equal angular points base BC bisected bisectors centre chord circumference circumscribed circle concyclic Constr Describe a circle diagonal diameter divided equal angles equal in area equiangular Euclid exterior angle find the locus given circle given point given straight line Given the base given triangle greater Hence hypotenuse inscribed circle isosceles triangle Let ABC line which joins magnitudes meet middle point nine-points circle opposite angle opposite sides orthocentre par¹ parallelogram parm pass pedal triangle perp perpendiculars drawn point of contact polygon produced Proof proportional PROPOSITION PROPOSITION 21 quadrilateral radius rect rectangle contained rectilineal figure regular polygon right angles segment shew shewn Similarly square straight line drawn tangent THEOREM triangle ABC vertex vertical angle Нур