Pythagorean hypotenuses as contraharmonic means

$c^2=a^2+b^2$	$c={\displaystyle \frac{u^2+v^2}{u+v}}$	N.B.
$5^2=3^2+4^2$	$5=(2^2+6^2)/(2+6)$	3
${10}^2=6^2+8^2$	$10=(6^2+{12}^2)/(6+12)$
${13}^2=5^2+{12}^2$	$13=(3^2+{15}^2)/(3+15)$	5
${15}^2=9^2+{12}^2$	$15=(9^2+{18}^2)/(9+18)$
${17}^2=8^2+{15}^2$	$17=(5^2+{20}^2)/(5+20)$	5
${20}^2={12}^2+{16}^2$	$20=(8^2+{24}^2)/(8+24)$
${25}^2=7^2+{24}^2$	$25=(4^2+{28}^2)/(4+28)$	7
${26}^2={10}^2+{24}^2$	$26=(6^2+{30}^2)/(6+30)$
${29}^2={20}^2+{21}^2$	$29=({14}^2+{35}^2)/(14+35)$	7
${30}^2={18}^2+{24}^2$	$30=({12}^2+{36}^2)/(12+36)$
${34}^2={16}^2+{30}^2$	$34=({10}^2+{40}^2)/(10+40)$	5
${35}^2={21}^2+{28}^2$	$35=({14}^2+{42}^2)/(14+42)$
${37}^2={12}^2+{35}^2$	$37=({30}^2+{42}^2)/(30+42)$	7
${39}^2={15}^2+{36}^2$	$39=(9^2+{45}^2)/(9+45)$
${40}^2={24}^2+{32}^2$	$40=({16}^2+{48}^2)/(16+48)$
${41}^2=9^2+{40}^2$	$41=({36}^2+{45}^2)/(36+45)$	3
${50}^2={14}^2+{48}^2$	$50=({42}^2+{56}^2)/(42+56)$	7
${51}^2={24}^2+{45}^2$	$51=({15}^2+{60}^2)/(15+60)$
${52}^2={20}^2+{48}^2$	$52=({12}^2+{60}^2)/(12+60)$	3
${53}^2={28}^2+{45}^2$	$53=({18}^2+{63}^2)/(18+63)$	7
${55}^2={33}^2+{44}^2$	$55=({22}^2+{66}^2)/(22+66)$
${58}^2={40}^2+{42}^2$	$58=({30}^2+{70}^2)/(30+70)$	7
${60}^2={36}^2+{48}^2$	$60=({24}^2+{72}^2)/(24+72)$
${61}^2={11}^2+{60}^2$	$61=(6^2+{66}^2)/(6+66)$	11
${61}^2={11}^2+{60}^2$	$61=({55}^2+{66}^2)/(55+66)$	11
${65}^2={39}^2+{52}^2$	$65=({26}^2+{78}^2)/(26+78)$
${68}^2={32}^2+{60}^2$	$68=({20}^2+{80}^2)/(20+80)$
${70}^2={42}^2+{56}^2$	$70=({28}^2+{84}^2)/(28+84)$
${73}^2={48}^2+{55}^2$	$73=({40}^2+{88}^2)/(40+88)$	11
${74}^2={24}^2+{70}^2$	$74=({14}^2+{84}^2)/(14+84)$	7
${75}^2={21}^2+{72}^2$	$75=({12}^2+{84}^2)/(12+84)$	7
${78}^2={30}^2+{72}^2$	$78=({18}^2+{90}^2)/(18+90)$
${80}^2={48}^2+{64}^2$	$80=({32}^2+{96}^2)/(32+96)$
${82}^2={18}^2+{80}^2$	$82=({10}^2+{90}^2)/(10+90)$	3
${85}^2={40}^2+{75}^2$	$85=({25}^2+{100}^2)/(25+100)$
${87}^2={60}^2+{63}^2$	$87=({42}^2+{105}^2)/(42+105)$	7
${89}^2={39}^2+{80}^2$	$89=({24}^2+{104}^2)/(24+104)$	13
${90}^2={54}^2+{72}^2$	$90=({36}^2+{108}^2)/(36+108)$
${91}^2={35}^2+{84}^2$	$91=({21}^2+{105}^2)/(21+105)$
${95}^2={57}^2+{76}^2$	$95=({38}^2+{114}^2)/(38+114)$	19
${97}^2={72}^2+{65}^2$	$97=({45}^2+{117}^2)/(45+117)$	13
${100}^2={60}^2+{80}^2$	$100=({40}^2+{120}^2)/(40+120)$