Full text: Appeltauer, Ignatius: Elementorum matheseos purae pars prima continens algebram

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283. §. Theorema. 
Areae figurarum similium se habent uti 
quadrata laterum homologorum, seu diagona 
lium homologarum. (Fig. 156.) 
Dem. Dividantur figurae similes ABCDE, 
FGHKL diagonalibus homologis in triangula 
similia, et erit triangulum ABC: FGH 
AB: FG. 
ACD: FHK — CD: HK — AB: FG. 
2 
— 2. 
ADE: FKL — DE: KL — AB: FG. 
Cum ergo triangula homologa inter se ean 
dem habeant rationem, erit summa anteceden 
tium ABC + ACD + ADE, seu area figurae pri 
mae, ad summam consequentium FGH + FHK 
+ FKL, seu aream figurae secundae, uti ABC 
ad FGH, vel uti AB: FG; id est uti quadrata la 
terum homologorum; vel etiam ut quadrata dia 
gonalium homologarum AC: FH, quia diago 
nales sunt in ratione laterum. 
284. §. Theorema. 
Si latera homologa trium figurarum simi, 
lium constituant triangulum rectangulum ABC, 
figura super hypothenusa aequalis erit figuris 
super cathetis simul sumtis. (Fig. 157.) 
Dem. Areae figurarum super hypothenusa AC, 
et super cathetis AB, BC designentur literis R,
	        
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