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A single program deck, with individual subroutines marked. The markings show the effects of editing, as cards are replaced or reordered. Many early programming languages, including FORTRAN, COBOL and the various IBM assembler languages, used only the first 72 columns of a card – a tradition that traces back to the IBM 711 card reader used on the IBM 704/709/7090/7094 series (especially the ...
From original triangle, ΔA 1 DB 1: Sketch Cayley diagram. Using parallelograms, find A 2 and B 3 O A A 1 DA 2 and O B B 1 DB 3. Using similar triangles, find C 2 and C 3 ΔA 2 C 2 D and ΔDC 3 B 3. Using a parallelogram, find O C O C C 2 DC 3. Check similar triangles ΔO A O C O B. Separate left and right cognate. Put dimensions on Cayley diagram.
Any two equilateral triangles are similar. Two triangles, both similar to a third triangle, are similar to each other (transitivity of similarity of triangles). Corresponding altitudes of similar triangles have the same ratio as the corresponding sides. Two right triangles are similar if the hypotenuse and one other side have lengths in the ...
English: Simplified version of similar triangles proof for Pythagoras' theorem. In triangle ACB, angle ACB is the right angle. CH is a perpendicular on hypotenuse AB of triangle ACB. In triangle AHC and triangle ACB, ∠AHC=∠ACB as each is a right angle. ∠HAC=∠CAB as they are common angles at vertex A.
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Area of triangle C = sum of areas of A and B. All three right triangles are similar, so all three areas are proportional to the side bordering the centre triangle. Hence, α(a2 + b2) = α c2, or dividing by α, we have Pythagoras' theorem.
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