Notes of lessons on the Herbartian method (based on Herbart's plan) . ( -&? u*. 1 a*. • 1be stated. W ^t-angled tnangle. (a) Square. .(e) Presentation. 1. Analysis of Enunciation. c Right-angled -j Square described on hypotenuse. I Squares described on to be (Square on hypo- f sum of square on otherproved. \ tenuse = [ sides. 2. Construction. On BC describe square BDEC (I. 46), and on BA, ACdescribe the squares BAGF, ACKH. Through A draw AL parallel to BD or CE (I. 31).Join AD, FC. 198 Notes on Herbartian Method. Proof,(a) Because each of angles BAC
Notes of lessons on the Herbartian method (based on Herbart's plan) . ( -&? u*. 1 a*. • 1be stated. W ^t-angled tnangle. (a) Square. .(e) Presentation. 1. Analysis of Enunciation. c Right-angled -j Square described on hypotenuse. I Squares described on to be (Square on hypo- f sum of square on otherproved. \ tenuse = [ sides. 2. Construction. On BC describe square BDEC (I. 46), and on BA, ACdescribe the squares BAGF, ACKH. Through A draw AL parallel to BD or CE (I. 31).Join AD, FC. 198 Notes on Herbartian Method. Proof,(a) Because each of angles BAC and BAG is a rightangle, therefore CA, AG are in same straight line (I. 14). Now angle CBD= angle FBA (Axiom11), for each of them isa right angle. Add toeach angle ABC, thenangle ABD = angle FBC.(b) Then in triangles ABDand FBC, because AB= FB, BD = BC, andangle ABD = angle FBC,therefore triangle ABD= triangle FBC (I. 4). (c) Now parallelogram BL is double of triangle ABD, because they are on same base, BD, and betweensame parallels, BD and AL (I. 41). And squareGB is double of triangle FBC, for they are onsame base FB and between same parallels FB andCG (I. 41). But doubles of equals are equal (Axiom6). Therefore parallelogram BL = square GB. (d) In a similar way by joining AE, BK, it can be shown that parallelogram CL is equal to square CH,therefore whole square BE = sum of squares GB,HC—that is, square on hypotenuse BC = to sum ofsquares described on two sides BA, AC.—() III. Association. Propositions, etc., used in proof. IV. Recapitu
Size: 1431px × 1747px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1900, bookpublisherlondo, bookyear1902
